Trigonometry

• Averaging Two Angles [Kathy, 06/08/1999]
  How do you take the average of two or more angles?

• Basics of Trigonometry [Coley, 12/12/2001]
  Why is trigonometry important? How is it used in the real world?

• Calculating Height in the Air [Bobby, 11/14/2001]
  I need to know the formula for calculating the height of an object, like how high in the air an object is.

• Changing a Trigonometric Graph [Wang, 08/06/1998]
  How do you graph: -cos 2x / 2?

• Curious Property of a Regular Heptagon [McCready, 04/06/2001]
  How can I prove that in a regular heptagon ABCDEFG, (1/AB)=(1/AC)+(1/ AD)?

• Deriving the Dot Product [Nick, 09/17/1998]
  Can you explain how to derive formula for the dot product?

• Deriving Sines of 30, 45, 60 and 90 Degrees [Michael, 06/02/1999]
  Where do the values for sin 30, sin 60, etc. come from?

• Explanation of Sine and Cosine [Mishra, 7/30/1996]
  I am having trouble with the topics of sine and cosine.

• Find Angle Given 3 Sides, NOT Using Law of Cosines [Diane, 12/18/2001]
  Why doesn't it work to use proportions?

• Flying a Kite [Duvall, 5/23/1996]
  Find the angle of elevation of a kite...

• Geometry vs. Trigonometry [Tipledan, 07/14/1997]
  What is the difference between trigonometry and geometry?

• History and Uses of Trigonometry [Pietruschka, 9/10/1995]
  What is trigonometry?

• Latin Origins of Trig Functions [Taing, 11/20/1998]
  What are the etymologies of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent?

• Length of a Triangle's Sides [Rappard, 1/23/1995]
  I have a triangle problem for you to solve: The lengths of the three sides of a triangle could be...

• Proving Identities Rigorously [Robert, 01/23/2002]
  I've been taught that the proper way to work on identities is to work with one side at a time only.

• Pythagorean Theorem and non-Right Triangles [Katy, 03/09/2002]
  Why doesn't the Pythagorean theorem work for triangles other than right triangles?

• Sine and Cosine Without a Calculator [Paul, 9/2/1996]
  How do I find sines and cosines without using a calculator?

• Sine, Co-sine, and Tangent: SOHCAHTOA [Angie, 03/28/1999]
  I am having trouble figuring out what to use when solving a triangle problem.

• Techniques of Integration - Change of Variables [Jenny, 02/17/1999]
  Solve: (integral sign) sin 2x/ sq rt (9-cos^4 x) dx .

• Trig Identities [Husik, 11/5/1994]
  I am a junior in High School and currently taking a pre-calc. course. We started the year with trig. identities. What confuses me is how to find the exact value (i.e, not a decimal answer) of an angle (in radians or degrees) QUICKLY. For several of our problems we need to know almost instantaneously the value of say, sec 15, sin 45, cos 60, etc. Instead of drawing a triangle on a cartesian plane and using the 30x30x60 or 45x45x90 rules, is there an easier way to derive the answers to these questions quickly?

• Trigonometric Functions and the Unit Circle [Allison, 05/22/2000]
  Why don't sine and cosine graphs have values greater than 1 or less than -1? Why does the tangent graph have asymptotes? How do the trig functions relate to the unit circle?

• Trigonometric Identities [Charlotte, 11/13/1997]
  Do you have any suggestions for finding an easy way to remember them that I could apply to all identities?

• Trigonometry in a Nutshell [Jimmy, 04/11/2001]
  What is trigonometry? Can you give me some problems and examples? What does trigonometry have to do with circles? with waves?

• Trigonometry: Positive vs. Negative [Cookies, 5/31/1996]
  The problem: tan x = 5/12 and sec x = -13/12

• The Unit Circle [Zeese, 4/2/1996]
  Could you describe how to "read" the unit circle?

• Volume of a Cylindrical Tank [Blockwook, 2/3/1995]
  I have to keep an inventory of how much is kept in a farm of tanks outside my school. The tanks are cylindrical, which would be no problem if the were standing on end...

• What is Arctan? [Sueshi, 8/28/1996]
  For the function f(x) = sin (arctan x), is sin the same as arctan X?

• Why Sine, Cosine, and Tangent? [Sara, 11/29/2001]
  Why does sine equal opp/hyp, cos equal adj/hyp, and tan equal adj/opp?

• Trig functions [Yuan, 11/22/1994]
  What is the definition of sine, and the other trig functions? I understand how to get it, but why was it chosen to be like that? How come all triangles have this property? Does it have something to do with the fact they all have 180 degrees?

• Sines and equations [Toub, 12/3/1994]
  I am a tenth grade student taking AMF (advanced mathematical functions) and was given the problem: 0<=X<=150; when does the Sin 8X = Sin X? I had no problem doing this on my graphing calculator, and finding the intersects between the functions, but is there any way to do this by using some sort of equation?

• Inverse trig functions [Hechenbleikner, 12/14/1994]
  I am trying to evaluate this: cot[sin^-1 (-1) + 2sec^-1 (-2)] In other words... cotangent of inverse sine of negative one plus two times inverse secant of negative 2.

• Pythagorean and Other Triangle Theorems [Murarka, 1/6/1995]
  Could you please show me the proof for the Pythagorean Theorem and list the other triangle theorems that are based on it?

• How Tall is the Building on the Hill? [Carmon, 1/19/1995]
  A building is 30 meters high and is on top of a hill. The angles of elevation of the top and bottom of the building from a point at the foot of the hill are 64 degrees and 58 degrees respectively. How high is the hill?

• Two Trigonometry Questions [Li, 1/22/1995]
  What is sin60 * cos60, and tan45 * tan3?

• Which Side is Longer? [Cohrs, 1/27/1995]
  You are given a quadrilateral, ABCD, with diagonal DB, angle ADC = 90, angle DBC = 43, angle C = 91, side AD = 9, side DC = 9. Find which is longer AB or AD.

• Tangent and Secant [Casey, 2/2/1995]
  I need help with the following problem: tan b + cot b = sec b csc b

• Inscribed Circle [bfeltenb, 3/18/1995]
  I need the formula to find the radius of an inscribed circle in an equilateral triangle. I also need to know the rationalization for the method.

• Trigonometry and Navigation [Francis, 3/29/1995]
  I have a research project to write about the uses of trigonometry in the field of navigation.

• Answer to a Trig Question [Ebert, 5/1/1995]
  What is the range of sin x = 1 / csc x ?

• Finding Shareware and Freeware for Teaching Trig [Stryjewski, 5/13/1995]
  Where can I find some shareware or freeware programs for teaching trigonometry (MS-DOS, Windows, or Mac)?

• Trigonometric Functions and Complex Numbers [Jones, 6/27/1995]
  Is there a solution to the following equation: Sin(a) = 5, where a = x + iy (complex value)?

• Trig and Inverse Trig Problems [Sharpe, 7/30/1995]
  I have three trig-related questions. Would it be possible to include explanations for solutions and some general rules?

• Trigonometry Problem [Cyril, 8/11/1995]
  A 12 metre ladder is inclined to the vertical at 48 degrees. How far is it from the base?

• Trigonometric Equation [Snell, 8/11/1995]
  Solve {x : 2sin(3x-1)+7 = 6.25, -Pi<x<Pi}.

• Using the Law of Cosines [Snell, 8/18/1995]
  Prove that, in any triangle, the sum of the squares of two sides is equal to twice the square on half the third side plus twice the square on the line joining the midpoint of the third side to its opposite vertex.

• Computing Sine and Cosine [Staerk, 8/27/1995]
  Is it possible to compute sine and cosine for a given angle without using a calculator or a sine table?

• Simplifying Trigonometric Expressions [Snell, 9/13/1995]
  A student asks for help simplifying and solving trigonometric expressions.

• Using the Laws of Sine and Cosine [Sten, 9/24/1995]
  How do I find the sine and cosine of pi/12?

• Using Graphs of Trigonometric Functions [Miller, 10/9/1995]
  We are working on csc, sec, and cot graphs, including how to change the sin, cos, and tan graphs to get them. I am interested in applications of these graphs. In what field would it be useful to know the period, the location of the asymptotes, and the domain of a sec graph?

• The Pythagorean Identity for Cosine [Kara, 11/11/1995]
  If Sin 9 = x , what is the solution and result of Cos9.cos18.cos36?

• Solving and Simplifying using Trig Identities [Anon., 12/5/1995]
  Could you please help? 1. Solve for x: 20.0^(3x) = 85.0 2. Simplify: 1 + (sec^2(@) / cos^2(@)) 3. Show that tan^4(y) - sec^4(y) = 1 - 2sec^2(y)

• Value of Angle DBC [Aviel, 1/23/1996]
  Imagine a triangle ABC on which angles B and C are equal to 80...

• Formulas for Sine and Cosine [Allman, 1/24/1996]
  What are the formulas for finding sin, cos, and tan in terms of theta?

• Circumference of a Globe [Oldenburg, 1/27/1996]
  How do you derive a formula to find the circumference of a large globe hung 25 feet in the air?

• Changes in the Cosine Curve [Sabrina, 1/27/1996]
  I need information on the changes in the cosine curve, especially on the change in amplitude and the period of revolution and phase shift.

• Trigonometric Formulas [Happer, 2/1/1996]
  My question concerns trigonometric formulas. How do I show how the double angle formulas are derived from the compound angle formulas?

• De Moivre's Theorem [Iquinds, 2/10/1996]
  What is the usefulness of de Moivre's theorem?

• Finding the Length of an Arc [Griggs, 2/14/1996]
  Find the length of an arc that subtends an angle of measure 70 degrees on a circle of diameter 15 cm., and find the area of that sector.

• Factoring with Trigonometry [Colaluca, 3/5/1996]
  4tan^2X + 7tanX - 2 = 0

• Solving a Trig Equation [Nawaz, 3/11/1996]
  (sin (alpa))/(alpha) = ?

• Asin/acos/atan for Complex Numbers [Justen, 3/27/1996]
  How do you find asin(x+iy), acos(x+iy), and atan(x+iy)?

• Another Trig Equation [Uriel, 3/30/1996]
  Solve: 4sinx + 3cosx = 4

• Solving a Periodic Function [Rich, 3/31/1996]
  Solve: sin2z = 5

• Finding What Number has the Sine of X [Morris, 4/12/1996]
  If the sine of y is x, is there a way to figure out what y is?

• Simplify Numerator and Denominator [Mehring, 4/15/1996]
  What is the algebra, or actually the trig that lets you simplify: -sin x + 1 / (1- sin x)^2

• Algebra and Trig Equation [Silva, 4/20/1996]
  I need to know how can I solve this equation: 1 = sin(3x) - cos(6x).

• Trig Word Problem [Atienza, 5/5/1996]
  Find the height of the tower...

• Trigonometry + Geometry [Kehatraj, 5/5/1996]
  A right angle triangle is blocking a circle and is being blocked by another circle...

• Graphing Trigonometry Equations [Smallwood, 5/15/1996]
  How do I graph this one: Sin A - Cos A ?

• Sine of an Angle and Opposite Side [Kwok, 5/17/1996]
  Given triangle ABC inscribed in a circle, prove why (sin A)/a equals the diameter of the circle.

• Etymology of Cosine [Allen, 5/21/1996]
  Where does cosine come from?

• Tangent of 90 Degrees [Pzgh, 5/24/1996]
  Why is the tangent of 90 degrees undefined?

• Integration [Wong, 5/29/1996]
  What does integral of (cos(x).x(cub).sinh(x)square).dx mean, and what's the answer?

• Trignometric Functions [Cookies, 5/31/1996]
  I have to find the four missing trig functions...

• Trigonometry -- Airport Word Problems [Hsu, 6/6/1996]
  A plane is 120 miles north and 85 miles east of an airport.... When an airplane leaves the runway, its angle of climb is 18 degrees and its speed is 275 feet per second...

• Three Trig Problems [Michael, 6/11/1996]
  1) Find tan x if ((sin x)^2)/3 + ((cos x)^2)/7 = (-sin(2x)+1)/10 2) A = 20 deg. and B = 25 deg. Find the value of (1+tanA)(1+tanB). 3) Evaluate cos 36 - cos 72.

• Sine, Cosine, Tangent; Four-meter Ladder [Hatcher, 6/15/1996]
  Is there any way to perform these functions without a calculator?

• How to Derive cos 72 [Brasher, 6/19/1996]
  Derive a radical expression for cos 72 using a 36-72-72 triangle.

• Trigonometry Proof [Brasher, 6/20/1996]
  Prove that if a,b,y > 0 and a+b+y = pi, then sin(2a)+sin(2b)+sin(2y) = 4(sin a)(sin b)(sin y)

• Trig Equation [Srdanovic, 6/22/1996]
  Solve for x: (cos(x))^2+(sin(x))^2 = (15*(cos(x))^2)/18)-(1/2)

• Given Tangent, Find Angle [Ishould, 7/2/1996]
  Given tan y=3n/4n, find y.

• Trigonometry Proof [Brandy, 7/18/1996]
  How do I prove that (cotX)(cosX)/(cotX + cosX) = (cosX)/(1 + sinX)?

• Integral of Trig. Function, Power [Gemilang, 7/19/1996]
  What is the integral of dx/cos^4 x?

• Proof of Trig Identity [Spencer, 7/24/1996]
  Prove (sin 2t + sin t)/(cos 2t + cos t + 1) = tan t is an identity.

• Using Trig Identities to Simplify [Will, 7/26/1996]
  How do I simplify ((sin @ - 1)/cos @) - (cos @/(sin @ -1)) ?

• Solution for Trig Equality [Sljr, 7/27/1996]
  Sin x = Cos x - what does it mean?

• Sin of More Than 2pi, 360 Degrees [emsmdt05, 8/6/1996]
  How do you find the sin of 2020?

• Finding Arc Sin [Rohland, 8/13/1996]
  How can I use sin, cos, tan, and arctan to define arcsin and arccos?

• Algebraic Expression for cos(arctan(x)/3) [Arno, 8/15/1996]
  How do I find an algebraic expression for cos(arctan(x)/3) so that I can get rid of the trigonometric operands?

• What is Trigonometry? [Aziebell, 8/20/1996]
  What is trigonometry, and what is it used for?

• Squares and Triangles: a Proof [Horrocks, 8/23/1997]
  Two points lie within or on the boundary of a square. Prove that the length of at least one of the lines...

• Angle, Side Length of a Triangle [Inman, 9/4/1996]
  What is the relation between the angles and side lengths of a triangle?

• Finding Angles [Caldwell, 9/6/1996]
  Given the side lengths of a right triangle, how do I compute the angle measures?

• Finding Values of x for Trig Equation [Rgg, 9/11/1996]
  How do I find the values of x to make: tan x = -x/((16-x^2)^.5)) true?

• Trig Functions [Turner, 9/29/1996]
  How do you know when to use sine, cosine, and tangent?

• Sine/Cosine Equations [Durrett, 10/23/1996]
  Are there equations for sine or cosine?

• Vertices of an Octagon [Murthy, 10/29/1996]
  Find the coordinates of the vertices of an octagon with center (0,0) when it is inscribed in a square.

• Train in the Rain [Josarge, 11/21/1996]
  Given a train moving in the rain, determine the actual velocity and direction of the raindrops/the train from how raindrops appear on the train windows.

• Calculators and Trig Functions [Kuhn, 12/03/1996]
  How do calculators solve trigonometric functions? Is there any way to determine the y value on a graph of the arc subtended by the angle theta?

• Complex Numbers and Trigonometry [Smith, 12/25/1996]
  If x is a real number, ArcSin(Sin(x)) = x. If z is a complex number, ArcSin(Sin(z)) does not equal z. Why?

• Finding Coordinates [Rounceville, 12/31/1996]
  Given two intersecting line segments, the angle they form at their intersection, the coordinates of one endpoint and those of the intersection, and the length of one of the line segments, how do you determine the coordinates of the remaining endpoint?

• Trigonometry Without Calculators [Gollapalli, 01/06/1997]
  How do you find Cos[40] without a calculator?

• Trigonometry Identities [Barder, 01/07/1997]
  Verify the identity sin(x+y+z) = sinx cosy coxz + cosx siny cosz + cosx cosy sinz - sinx siny sinz.

• Proving Trigonometry Identities [Baine, 01/07/1997]
  Prove these trigonometry identities (tan x+cot x)tan x = sec^2 x and (1+cos x)(1-cos x) = sin^2 x

• Right Triangle Kite Problem [Wilson, 01/16/1997]
  When flying a kite, 150 ft. makes an an angle of 51 degrees with the ground. Assume the string is straight; how is the kite?

• Secant, Cosecant, and Cotangent [Hagler, 01/16/1997]
  How do you understand the secant, cosecant, and cotangent functions?

• Euler Equation [Davis, 01/21/1997]
  What is the meaning behind e^(pi*i) = -1?

• Angle of Elevation [David, 01/22/1997]
  A tree 66 meters high casts a 44-meter shadow. Find the angle of elevation of the sun.

• Computers and Trigonometric Functions [Hicks, 02/11/1997]
  How do computers and calculators calculate values for sine, cosine, and tangent?

• Expressing Arccos in Terms of Arctan [Neubert, 02/24/1997]
  How do you express Arccos in terms of Arctan?

• Triangular Garden [Ferguson, 03/18/1997]
  Find the length of a fence that runs from the right angle to the hypotenuse and separates the garden into two parts of equal perimeter.

• Formulas: Width, Side Length of Octagon [Perkins, 03/24/1997]
  Given the width of an octagon, what is the length of a side, and vice- versa?

• Trigonometry Mnemonic [Lois, 04/12/1997]
  How do you spell the trigonometry word that is something like SOCHOATOA? It means side over hypotenuse, etc.

• Trigonometry Proof [Ailsa, 04/21/1997]
  Prove that (sin 50 x cos 50)/tan 50 = sin^2 40.

• Terminal Side [Laura, 04/21/1997]
  Find cos(A) if the point (2,-3) is on the terminal side of A.

• Roots of a Complex Equation [Raylim, 04/28/1997]
  Given that cos t + isin t is the root of z^3 + az + b = 0 in which sin t is not equal to 0, and that a and b are real and not equal to zero, show that a + b^2 = 1.

• Proof of DeMoivre's Theorem [Liya, 05/01/1997]
  A typical induction proof: DeMoivre's theorem.

• Covariants [Vincent, 05/02/1997]
  Express tan(pi/2 + X) as a single function of X or as a constant.

• Graphing Trig Functions [Nem, 05/03/1997]
  How do you graph y = 3sin4x-3?

• Rotating a Point around an Angle [Chupachenko, 05/16/1997]
  How do you derive the formulas for rotating a point around an angle?

• The Square Root of i [Leif, 05/25/1997]
  What is the square root of i?

• Infinity or Undefined? [Hawkins, 06/21/1997]
  Why is the tangent of 90 degrees considered undefined instead of being considered infinite?

• Origin of the Terms Sine and Cosine [Kel, 07/02/1997]
  I assume the term tan comes from the word tangent, but where do the terms sine and cosine come from?

• Degree Measure of a Central Angle [Woods, 07/29/1997]
  Find the degree measure, to the nearest tenth, of a central angle whose intercepted arc measures 21 cm. in a circle of radius 4 cm.

• Octagon Formula [Ecker, 07/30/1997]
  If you're building an octagon on a 12-foot radius, what is the length of each side?

• Trigonometry Identities [Lozano, 07/30/1997]
  I have a problem with these identities...

• Ferris Wheel [Rhiannon, 08/11/1997]
  How can you find how high in the air you are when on a ferris wheel at the 3 o'clock position?

• Why does a/SinA = b/SinB = c/SinC? [Gibson, 08/12/1997]
  I was just playing aroung with a proof of a triangle and came across the fact that a/SinA = b/SinB = c/SinC. Why?

• Solving Trig Problems [Tan, 08/18/1997]
  Find the value of Tan [(x+1)/(x-1)]^(-1) + Tan (x)^(-1).

• Arccos [Pierre-Marc, 08/23/1997]
  Please solve: Arc cos (cos y) + Arc sin (sin x) = y + x.

• Degrees, Minutes, Seconds [Vickers, 08/26/1997]
  I know that degrees are what you use to measure angles, but I thought minutes and seconds were time measurements...

• Two Airplanes [Gilbert, 08/28/1997]
  Draw a diagram using coordinate system with origin O - how far apart are the airplanes? Express the answer in radical form.

• Computing Angles of a Right Triangle [Silva, 09/04/1997]
  Is there a way to compute the other two angles of a right triangle without a calculator? If a table is required, where can I find it?

• Height of a Hill [Susruta, 09/06/1997]
  From the top of a hill, the angles of depression of two consecutive kilometre stones due east are 30 and 45 degrees.

• Euler Equation [Dale, 09/13/1997]
  Does the Euler equation still work if we decide to work in degrees? Is it arbitrary?

• Basic Trig Identities [Chen, 09/15/1997]
  If sin(theta) = 3/4, find sec. I tried the reciprocal identity, but that didn't work.

• Law of Cosines and Pythagorean Theorem [Moll, 09/23/1997]
  I would like to know how to calculate the angles in a triangle if all you know is the length of the three sides.

• Trigonometry Substitutions [Szollosy, 09/30/1997]
  I am having problems doing trig substitutions. Can you suggest any methods?

• Trigonometry, Logs and Map Projections [Lotter, 10/01/1997]
  I am trying to figure out the inverse function used by the Mercator map projection.

• Trig Problem: Sec A = -2 ... [Rausch, 10/20/1997]
  How can I find all the angles in the range between 0 and 2*pi radians that have a secant equal to -2?

• Logarithmic Equivalent of the Inverse Hybolic Cosine Function [Gurnell, 10/28/1997]
  I recently attempted a question which I think I have done wrong and I was wondering if there were a set formula for this problem...

• Complex Numbers, Trig Functions and Roots of 1 [Knobler, 10/30/1997]
  I'm convinced that, for a an arc of length x in radians: (cos x + i sin x)^(2 pi / x) = 1... It's cool but why does it work?

• Derivation of Law of Sines and Cosines [Yuan, 11/02/1997]
  How do you derive the law of sines and the law of cosines?

• Optimization: Minimum Area [Yamashita, 11/07/1997]
  How do you fold a piece of paper (rect. with width a and unlimited length) so one corner just reaches the righthand side for minimum area?

• Integration of Sin(x^2) [Joshua, 11/10/1997]
  I have been given the solution in the form of Frensel's Sin, but it explains nothing about how it was integrated. I am not looking for an equation, I am looking for a reason!

• Trigonometric Identities [Schoenherr, 11/12/1997]
  What is the best way to solve verification problems?

• Product Sum and Difference Formulae [Agarwal, 11/20/1997]
  cos6theta+6cos4theta+15cos2theta+10/cos5theta+5cos3theta+10cos theta = 2 cos theta.

• Art Gallery Problem [Cloutier, 11/30/1997]
  A picture is two meters high and is hanging so the bottom of the picture is one meter above eye level. How far from the wall should you stand so the angle of vision occupied by the picture is a maximum?

• De Moivre's Theorem [Pountney, 12/03/1997]
  Prove De Moivres theorem: - (cos(x)+isin(x))^n = cos(nx) + isin(nx) .

• Why Radians? [Munroe, 12/03/1997]
  Why use radians to measure angles over degrees?

• Trigonometric Identities [Henderson, 12/10/1997]
  How do you prove sin(t+s)sin(t-s) = sin^2t-sin^2s ?

• Inner Product [Goga, 12/10/1997]
  How can I find the angles of the triangle formed by three points using the inner product?

• Cosine Addition Formula [Memon, 12/13/1997]
  How can you prove the addition formula for cosine by using right triangles?

• Solving Trigonometric Equations in Radians [Alex, 12/14/1997]
  Solve for theta in radians to 2 decimals if 0 < theta < 2 pi tan theta = -0.318.

• How the Trig Functions Got their Names [Becker, 12/14/1997]
  I can guess why three of the trig functions are called cosine, cotangent, and cosecant. But why were the other three named the sine, the tangent, and the secant?

• Find a Function, Integrals [Lanka, 12/17/1997]
  Suppose the graph of f has the formula f(x)=-x+1 for 0<=x<=1; x-1 for 1<x<=2 ...

• Sine numbers in Charts for Angles [Oswalt, 12/22/1997]
  I am a toolmaker and I'd like to know where the numbers in sine charts or on a calculator come from.

• The Shortest Crease [Shanger, 12/29/1997]
  A piece of paper is 6 units one side and 25 units on another side...

• Cosine Approximations [Freedenberg, 12/29/1997]
  You derived a cubic equation for cosine of 40 degrees - did you know this approximation...?

• Trig Identities and Double Angles [Sandiford, 01/04/1998]
  Prove that sec2A + tan2A = cosA + sinA / cosA - sinA.

• Trigonometric Identity [Smith, 02/12/1998]
  Prove that sin 7x = 7(sin x) - 56(sin x)^3 + 112(sin x)^5 - (sin x)^7.

• Pythagorean Identity of Trigonometry [Swaine, 02/16/1998]
  Proof of the trigonometry identity sin^2 + cos^2 = 1.

• Trigonometry Identity [Shweta, 02/20/1998]
  Prove a*cos(A) + b*cos(B) + c*cos(C) = 4R*sin(A)*sin(B)*sin(C).

• Computing sin without a Chart [Ranum, 02/23/1998]
  Is there a formula for converting a sin angle back to degrees?

• Determining Measure of Angle Without Tables or Calculators [Vooys, 03/05/1998]
  Arctangent formula for determining measure of angle XOP, given P(x,y) on the unit circle.

• Proof of a Trig Identity [Hebert, 03/13/1998]
  Proving that (1 + sinX + cosX)/(1 + sinX - cosX) = (1 + cosX)/sinX.

• Arccos Algorithms and Computer Calculators [Gilson, 03/21/1998]
  I need an algorithm to find the arccos of a value.

• Solving Right Triangles [Adkison, 03/25/1998]
  How do you know when to use sin, cos, or tan when solving right triangles?

• Trig Proof: Two Methods [J.W., 03/26/1998]
  Prove: (1 + sin x + cos x)/(1 - sin x + cos x) = (1 + sin x)/cos x.

• Triangles and Law of Sines [Heathe, 03/27/1998]
  How can you use the Law of Sines to produce more than one triangle?

• Explaining the Dot Product [Waycaster, 04/05/1998]
  Exactly what does the dot product represent?

• Deriving a Trig Identity [Yandell, 04/09/1998]
  Can you derive the identity tan(x)+tan(y)+tan(z) = tan(x)tan(y)tan(z), where x, y, and z are angles of a triangle?

• Trig Proof - Newton's Formula [Jay, 04/09/1998]
  Can you prove that: (a - b)/c = sin ((1/2)(A - B))/cos ((1/2)(C))?

• Trigonometric Functions and Euler's Identity [Jung-bok, 04/10/1998]
  We need to prove three trigonometric functions in various ways.

• Maximizing Horizontal Distance [Carter, 04/10/1998]
  Using algebra, prove that an object needs to be thrown at 45 degrees to travel the greatest possible horizontal distance.

• Over the Right Field Fence [Porter, 04/11/1998]
  What would be the distance of a hit from home base over the top of a 30 ft. high right field fence?

• Finding the Area of a Regular Pentagon [Gilman, 04/15/1998]
  How can you find the area of a regular pentagon given only the length of one side?

• Calculating Cosine Values Graphically and Algebraically [Lindsey, 05/01/1998]
  If cos(t) = -2/5, what are cos(-t), sin(pi/2 - t), cos(t + 2pi), and cos(t - 2pi)?

• Trig Functions of Angles Expressed in Degrees and Minutes [Retzack, 05/04/1998]
  Using calculators to evaluate trigonometry functions of angles expressed in degrees and minutes.

• Mnemonic For Remembering Formulas for Sin, Cos, Tan [Burd, 05/15/1998]
  The story of Chief Soh Cah Toa.

• Trig Functions in Three Problems: Graphing, Solving, and Factoring [Carolyn, 05/15/1998]
  Graphing sin(x) - cos(x), solving sqrt(3)*cos(x) = sin(x), and factoring.

• Proving Sine Identities [Susan, 05/16/1998]
  Can you help me prove the trigonometric identities for sin(A+B), sin(2A), and sin(A/2)?

• Using the Law of Cosines [Dan, 05/21/1998]
  Given the length of three sides of a triangle, how can I find the angle between any two of the sides?

• Simplifying Expressions with Double-Angle Formulas [Pickett, 05/25/1998]
  Using double-angle formulas, can you help me express 1 - 2*sin^2(4x) and 2*sin(5x)*cos(5x) as a single function?

• Graph of Circle as a Function [Thompson, 05/30/1998]
  The graph of a circle is not a function because it fails the vertical line test. How could you make it a function?

• Simplifying Trigonometric Equations [Keenan, 06/02/1998]
  I need help simplyifying the following trigonmetric equation and proving the trigonometric identity...

• Cycloids [Marek, 06/16/1998]
  What are cycloids, and how do they differ from sine curves?

• Surface Area of a Cone [Schultz, 06/18/1998]
  What is the formula for the surface area of a cone?

• Hyperbolic Functions [Yoshi, 06/27/1998]
  What does the inverse of sinh or cosh mean?

• The Height of a Distant Tree [Kostia, 07/08/1998]
  If a tree is 1 mile away, and I see it as 5 cm tall, how can I find its real height?

• Two Problems on Tangents [Wah, 07/09/1998]
  How can you show that the arc and the angle formed by two tangents are supplementary? Find the radius of circle O, given the following...

• Tan 90 [Chung, 07/10/1998]
  Why is tan 90 undefined?

• Vector Angles: Prove A.B = |A||B|cosA [Bryan, 07/13/1998]
  I just finished my pre-calc class, and at the end we covered vectors...

• Applications of Trigonometry [Lee, 07/19/1998]
  Can you help me with the following trigonometry questions on: vectors and airspeed, the area of a triangle, and the sixth roots of -64?

• Using Sine and Tangent to Find Pi [Marshall, 08/01/1998]
  How can I determine the sine or tangent of an angle without using a calculator?

• Trigonometry and Complex Numbers [Wang, 08/05/1998]
  Simplify (sqrt 3 - i)^7 into the form a + bi using DeMoivre's Theorem.

• DeMoivre's Formula [Lukens, 08/13/1998]
  Can you explain DeMoivre's Theorem?

• Finding Values by Hand [Victor, 08/26/1998]
  How can you find the exact value for sin 18, cos pi/16, etc. without using a calculator?

• Deriving Identities [McLean, 08/26/1998]
  I'm supposed to derive the identity for sin 3x in terms of sin x.

• Area of a Regular Octagon [Park, 08/31/1998]
  A proof of the formula.

• Sine Series [Meyer, 09/09/1998]
  What does sin1*sin2*sin3***sin179 equal in degrees?

• Tutorial material/books/help [Rogers, 11/16/1998]
  Can you suggest something I can order or download to help me with trigonometry and pre-calculus?

• Right Triangle Sides [Bobbi, 09/14/1998]
  To use SOHCOHTOA, I need help finding which sides are opposite and adjacent.

• Shot Out of a Cannon [Langridge, 10/12/1998]
  A performer is shot out of a cannon at 30 degrees from the horizontal, to land 20 meters away... What should his initial speed be?

• Hyperbolic Functions [Weber, 10/14/1998]
  Can you explain hyperbolic functions? How are they defined? How do you evaluate them?

• Trig Based on the Unit Square [Barr, 10/22/1998]
  Why are the sine and cosine graphs defined in a unit circle? Why not a unit square or any other geometric shape?

• Finding Intervals in Trig Graphs [Sara, 10/25/1998]
  Can you help me with graphing sine and cosine functions? How do you mark off the intervals?

• Proving Trig Identities [Moscoe, 11/15/1998]
  How do I prove trig identities like sin^6x+cos^6x = 1-3sin^2xcos^2x?

• Double- and Half-Angle Identities [Hefner, 11/24/1998]
  Use the double- and half-angle trigonometry formulas to find the exact values for sin(5 pi/12) and cos(7 pi/8).

• Derivations of Heron's Formula [Hath, 11/24/1998]
  How is Heron's formula (Hero's formula) derived?

• Which Quadrant in the Unit Circle? [Rosalynn, 11/30/1998]
  Find the quadrant in which C(s) is located. Example: C(14pi/3)= C(2pi/ 3). Thus, C(14pi/3) is in quadrant II.

• Trigonometry and the Chain Rule [Amanda, 12/01/1998]
  I need help differentiating expressions such as: y = 2 csc^3(sqrt(x)) and y = x/2 - (sin (2x))/4. Where does the chain rule fit in?

• Equations for the Paths of Four Lady Bugs [Morcombe, 12/02/1998]
  Four ladybugs travel from the corners of a square towards the center. Find the equations that describe the path.

• Perimeter of an Inscribed Regular Polygon [Willems, 12/10/1998]
  What is the formula for the perimeter of a regular polygon inscribed inside a circle?

• Trisected Hypotenuse of a Triangle [Nuse, 12/20/1998]
  In right triangle ABC, with C as the right angle... what is the length of AB (the hypotenuse)?

• Trigonometry And Music [Elizabeth, 12/21/1998]
  How is trigonometry used in music?

• Demonstrating Sin, Cos, Tan on the Unit Circle [Miller, 12/30/1998]
  Can you recommend a good way to demonstrate the trig functions sine, cosine, and tangent? What about on the unit circle?

• Horizontal Gas Tank Content Formula [Austrino, 01/17/1999]
  Can you help me find a formula to measure the volume of gas left in a horizontal gas tank given the height of the gas and the dimensions of the tank?

• Law of Tangents [Veatch, 01/22/1999]
  What is the law of tangents? How is it derived?

• Deriving the Arcsin Formula [Suzio, 01/24/1999]
  Why is the arcsin(A) = pi/2 + bi, for some b? How can you derive the inverse sine formula (i.e.: arcsin)?

• Non-negative Acute Angle [Stoerger, 01/26/1999]
  How can you express the sine or cosine of any angle as the sine or cosine of a non-negative acute angle? Why would they be equal?

• Steiner-Lehmus Theorem [McIntosh, 01/28/1999]
  I have a proof about an isosceles triangle that I just can't figure out...

• Applications of Non-antidifferentiable Functions [Mekisha, 01/29/1999]
  What are some of the real life applications of the functions sin (x)/ x, e^(-x^2), and sin (x^2)?

• Miter Angle of a Pipe [Bruce, 02/10/1999]
  Find the miter angle of a pipe of certain shape.

• Inverse Functions [Knote, 02/11/1999]
  If y = arcsec(x) then what does x equal? How is this problem related to inverse functions?

• Proving Trigonometric Identities [Calsyn, 02/12/1999]
  Tips on proving trigonometric identities, as well as a good general procedure to use, worked out on cos^4(x) - sin^4(x) = cos(2*x).

• Integration [Crys, 02/17/1999]
  Integrate x*tan^2 x with respect to x.

• Phase Shift in Sine Function [Corine, 02/19/1999]
  I am stuck on y = sin(4x+pi/3)... Could you please show me an example of a shifted graph?

• Integration Hints [Scott, 02/23/1999]
  Can you help me integrate (cos[x])^4?

• Arctan and Polar Coordinates [Jim, 03/09/1999]
  What is arctan?

• 30-60-90 and 45-45-90 Triangles [Kristina, 03/15/1999]
  If I have a triangle that is 30-60-90 or 45-45-90, how do I find all the sides when given only one side? Where does trigonometry come in?

• Square Roots of Complex Numbers [Jaimee, 03/28/1999]
  Devise at least two methods for finding the square root of (a+bi).

• Where Will the Runners Meet? [Mize, 03/29/1999]
  Two runners, A and B, start 90 degrees away from each other on a circular track and run at the same speed. If Runner B decides to cut across the track, where will they meet?

• Catenary Curve [Stephen, 03/30/1999]
  Find the vertex of a catenary curve.

• What is the Longest Pole? [marinsek, 04/04/1999]
  A metal pole L ft long is pushed on the floor from one corridor into another corridor at a right angle...

• Related Rates - Clock Hands [Perry, 04/05/1999]
  How fast is the distance between the tips of the hands on a watch changing at one o'clock?

• Sine, Cosine, and Tangent on a Circle [Jongejan, 04/14/1999]
  Where are the sine, cosine, and tangent on a unit circle?

• Trig Identities [Was, 04/16/1999]
  I have to prove that cos 36 (or sin 54) = (1+sqrt(5))/4.

• Deriving the Haversine Formula [Neff, 04/21/1999]
  I need to write a program module to calculate distances given longitude and latitude data, trying to find an object within a mile's radius of its location.

• Finding the Third Side [Kat, 04/24/1999]
  Using trigonometry, how do you find a third side of a scalene triangle given two side measures and an angle measure?

• Given a Triangle with Angles a,b,c [kellogg, 05/03/1999]
  Show that cos(a)+cos(b)+cos(c) is less than or equal to 3/2.

• Angle of Sun's Rays [Mullan, 05/03/1999]
  How can you determine the angle at which the sun's light hits the earth at any given point?

• Trig Problems [Dietrich, 05/07/1999]
  What are the steps to follow in order to answer these questions? 1) cos2x = sinx; 2) cos2x = cosx...

• Deriving Trilinear Coordinates [Smith, 05/18/1999]
  How do you derive the trilinear coordinates of the orthocenter of a triangle?

• Tan, Cos, Sin [Siobhan, 05/21/1999]
  Please tell me about tan, sin, and cos. How do you know which one to use?

• Trigonometric Identities [Miller, 05/24/1999]
  How can I simplify trigonometric identity problems such as sin^ 2(theta) - 1?

• How High Did My Rocket Go? [Joey, 05/28/1999]
  We were 15 feet away from a rocket at launch and measured an angle of 89 degrees on the first launch and 67 degrees on the second. Can you tell me how high it went?

• Integration of Trigonometric Functions [Corenne, 05/28/1999]
  How can I integrate sin(x)sin(2x).dx ?

• Using Trigonometric Identities [Shannon, 05/31/1999]
  How can I prove that sin(4x) = 2sin(2x) - 8sin^3(x)cosx ?

• Surface Area of an Oblate Spheroid [Lisa, 06/02/1999]
  Could you please give an example of solving for the surface area of an oblate spheroid using the inverse hyperbolic sine function?

• Proving a Trigonometric Identity [Lamoureux, 06/06/1999]
  How can I prove the trigonometric identities cos(a+b)*cos(a-b) = cos^2a - sin^2b, and tan(x/2) = (1-cosx)/(sinx)?

• Deriving the Coordinates of the pi/6 Family [Kelly, 06/09/1999]
  How do you derive the coordinates of the pi/6 family on the unit circle, and why does this work?

• Ratios, Geometry, Trigonometry [Cathy, 06/10/1999]
  A homeschool teacher asks for help with triangles, flagpoles, and circles.

• Sin(x) = x? [Younes, 07/01/1999]
  Is it true that when x is very small (e.g. x = 10^-70), then sin(x) = x? Why?

• Trigonometry and the Earth [Mike, 07/13/1999]
  A woman 6 ft. tall stands at the edge of the ocean. The radius of the earth is 3960 miles. How far out can she see?

• Trigonometric Identiity [Stephen, 07/29/1999]
  Prove arcsin(-x)= -arcsin(x).

• Evaluating a Trigonometric Expression [Alireza, 07/31/1999]
  Can you help me evaluate tan (arcsin (3/5))?

• Proof of the Parallelogram Law [Kenneth, 08/07/1999]
  How do you prove the parallelogram law geometrically, without using vectors?

• Approximating Arcsin [Joel, 08/10/1999]
  Using the Taylor series, a polynomial, or interpolation to calculate arcsin.

• Shadow Moving Along a Wall [Kris, 08/16/1999]
  There is a light at the front of a circular arena. A boy starting from B runs at the rate of 3 m/s toward the center C. At what rate will his shadow be moving along the rear wall when he is halfway from B to C?

• Trig Function Domains [Ukachukwu, 08/23/1999]
  Which came first, trigonometry based on the simple triangle or trigonometry based on the triangle of the unit circle?

• Packing 4 Spheres Into a Tetrahedron [Lam, 09/03/99]
  How can I find the dimensions of the smallest tetrahedron that can serve as a container for 4 spheres packed as snugly as possible?

• Methods of Computing Trig Functions [Morgan, 09/07/99]
  What would I do to figure out the actual angle of C, without using a table or calculator, if I know that tan(C) = 4/3?

• Angles in Trig Functions: Significant Figures [Prendergast, 10/05/1999]
  Handling significant figures in angle measurements in trigonometry problems.

• Altitude of a Model Rocket [Swayze, 10/26/1999]
  I need an algebraic formula that determines the altitude of a rocket based upon inclination observations of three ground observers.

• Area of a Regular Octagon [Tahiliani, 10/27/1999]
  How do you find the area of a regular octagon?

• Origin of the Terms Sine, Cosine, Tangent, etc. [Natalie, 10/27/1999]
  Can you tell me the origin of the terms hypotenuse, sine, cosine, and tangent? Can you tell me how the trigonometric formulas for sine, cosine, and tangent came about?

• One- and Two-sided Polygons [Sue, 12/07/1999]
  Can you explain what a monogon and a digon are?

• Ambiguous Cases - Laws of Cosines and Sines [Feinman, 04/26/2000]
  When I try to use the law of cosines and the law of sines on triangle ABC, with sides of length a = 3.2, b = 4.3 and c = 5.1, I get two different answers.

• Circle on a Sphere Equation [Walker, 05/05/2000]
  How can I find an equation for all points that fall within a given radius from a single latitude and longitude on the surface of a sphere?

• Finding the Value of an Inverse Trig Function [Granados, 05/08/2000]
  How can I find the value of cot[sin^-1(4/5)]?

• Finding the Angle of a Vector [deKruif, 05/10/2000]
  How can I find the angle for a vector (x,y) that originates from the origin (0,0)?

• Drawing an Arrow [Sageryd, 05/11/2000]
  How can I find the coordinates of the edges of an arrowhead? I want a program to draw an arrowhead from a user-defined baseline, with the angle between the baseline and arrow side 30 degrees.

• Length of the Diagonals of a Parallelogram [Moose, 05/22/2000]
  A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How long are its diagonals?

• Solving an Equation with Sines and Exponents [Boisse, 05/24/2000]
  How can I solve the equation sin^2(exp(c-x)) + sin^2(exp(c+x)) = 0, where x is a (real) unknown and c is a real positive constant?

• The Exact Value of the Sine of 1 Degree [Ward, 05/24/2000]
  Has anyone ever figured out the exact value for the sine of 1 degree or pi/180 radians?

• Graphing Sine and Cosine [Bernadette, 07/07/2000]
  How do you graph equations that use the sine or cosine functions?

• Projectile Dynamics [Peter, 10/21/2000]
  A particle is projected with initial velocity v and angle theta in a parabolic path. How can I show that at time t, when the angle to the horizontal is gamma, tan(gamma) = tan(theta) - (gt/v) sec(theta)?

• Simulating Sound Waves [Kay, 10/27/2000]
  How can I simulate a sound wave that reaches a maximum height every seventh crest?

• Continued Fraction for Tan(x) [Joseph, 11/03/2000]
  Can you tell me why the "infinite continued fraction representation" for the tangent function works?

• Sine and Cosine Addition Formulas [Phara, 11/29/2000]
  Can you prove the addition formulas for sine and cosine? Also, if sin(2Q) = a, then what is sin(Q) + cos(Q) in terms of a?

• Double and Half-Angle Identities [Gardner, 12/08/2000]
  Why do we have to learn the double and half-angle identities? Why can't we just take the sine, cosine or tangent of double or half of the actual angle?

• The Sine of 1 Degree [Goldberg, 01/07/2001]
  How can I find an exact value for the sine of 1 degree using only the values of sine for special angles and the angle-addition formulas?

• Finding Sides and Angles [Yee, 01/22/2001]
  Can you determine the length of the hypotenuse and an acute interior angle of this right triangle?

• Circumference at a Given Latitude [Lynn, 01/26/2001]
  How can I calculate the circumference of a line around the earth (a circle) at 40 degrees north latitude?

• Circular Motion [Kim, 01/27/2001]
  Two problems: An electric hoist is being used to lift a piece of equipment... A car is moving at a rate of 50 miles per hour and the diameter of its wheels is 2.5 feet...

• Function Frequencies [Worrell, 02/03/2001]
  Why does the tangent function have twice the frequency of the sine and cosine functions?

• Arccos(x) + Arcsin(x) = Pi/2 [Susan, 02/04/2001]
  Prove that for all x between -1 and 1, arccos(x) + arcsin(x) = pi/2.

• Limit of Cos(Cos( ... Cos(x) ... ))) [Dellinger, 02/24/2001]
  Find the limit of a repeating trigonometric expression cos(cos( ... cos(x) ... )) as the number of cosines goes to infinity.

• Modeling Tides with Trigonometry [Holseth, 03/07/2001]
  How can I find a trigonometric equation that models the depth of the water at the end of a pier throughout the day, given the heights and times of low and high tide?

• Sine, Cosine, Tangent [Gale, 03/13/2001]
  What are sine, cosine, and tangent?

• X = TanX [Andrew, 03/21/2001]
  Show that x = tanx has an infinite number of solutions.

• Radians [Maddie, 03/22/2001]
  I have searched everywhere for the history behind radians. Why did they replace degrees?

• Height of the Plane [Komorowski, 03/29/2001]
  Towers A and B are 4.1 miles apart on level ground. A pilot finds the angles of depression to the towers to be 36.5 and 25 degrees, respectively. Find the height of the airplane.

• Trigonometric Equation for a Sequence [Gruber, 04/03/2001]
  I need an equation for the sequence 0, 0, 1, 0, 0, 1, 0, 0, 1, ... using the sine or cosine function.

• Simplifying Expressions with Trig Functions [Betsey, 04/04/2001]
  How can I solve problems like: 4 csc(3pi/4) - cot(-pi/4)?

• Summation Formulas for Trigonometric Functions [Aaron, 04/24/2001]
  How do you find the area under the curve of a trigonometric function using the definition of a limit and not an approximation? Are there summation formulas for trigonometric functions?

• Deriving Trig Functions; Taylor Series [Harold, 05/01/2001]
  How would I find, from first principles - no tables, no calculator - for example, 32 degrees? If I use a formula, how is it derived?

• Moving a Circle on a Polar Graph [Mike, 05/04/2001]
  How do you move a circle so the center is not (0,0), but to where the center can be (r,[theta])?

• Transforming Trig Functions [Alex, 05/08/2001]
  Express 3 sin x + 5 cos x in terms of sin x so that the graph is the same as the first equation.

• Radius of Circumscribed Circle [Peter, 05/11/2001]
  Where can I find a derivation of R = abc/4K?

• What's 'Arccos'? [Daniel, 06/17/2001]
  I'm trying to write a program in Visual Basic 6 about the distance calculation between two cities.

• Distance from A to B [Jay, 06/17/2001]
  The bearing of B from C is 254 degrees. The bearing of A from C is 344 degrees. The bearing of A from B is 32 degrees. The distance from A to C is 780 meters.

• Find the Cities [Rod, 06/19/2001]
  Given the latitudes and longitudes of Detroit, MI, and Miami, FL, find every city within 10 miles of a straight line between them.

• Standard Angles [Nagaraj, 08/09/2001]
  Why are 0, 30, 45, 60, and 90 degrees taken as standard angles in trigonometry? Why can't we take some other angles?

• The Top of the Tower [Ashley, 07/20/2001]
  Given a 300-mile-tall tower on the earth, how far away from it can you go before the top disappears below the horizon?

• Inverse Trigonometry [Robin, 08/22/2001]
  I can't find my mistake.

• Calculating the Angle of a Plank [Nick, 08/22/2001]
  Are there any equations that could be used to solve for a plank of known width?

• Octagon Side Lengths [Rob, 08/22/2001]
  If I know that the dimension of an octagon from one side to the other is 8 feet, how can I find the lengths of a side?

• What is the Relation between tan and tanh? [Barot, 08/25/2001]
  I want to know the relation between tangent and hyperbolic tangent.

• Sin x^2, Sin^2 x, (Sinx)^2 [Rob, 09/12/2001]
  What is the difference between sin x^2, sin^2 x, and (sinx)^2?

• Why Use Radians instead of Degrees? [Kanishka, 09/25/2001]
  Consider Maclaurin's theorem, from which we derive the Taylor series...

• Remembering Trig Functions [Kim, 09/27/2001]
  We have to memorize the sine, cosine, tangent, secant, cosecant, and cotangent for 30, 45, and 60 degrees for precalculus class. Do you have any tips on how to remember these?

• Precision in Measurement: Perfect Protractor? [Ivan, 10/16/2001]
  Given that protractors are expected to be accurate to the degree, and in some instances the minute or second, how are angles accurately constructed and marked?

• Two Dogs Pulling a Sled [Mike, 10/15/2001]
  What are the magnitude and direction of the force the person will have to exert on the sled to keep it moving along the centerline of the road at constant velocity?

• Etymologies of Algebra, Geometry, Trigonometry [Nikki, 10/22/2001]
  What are the origins and roots of the words geometry, algebra, and trigonometry?

• Trigonometry Terminology [Scott, 10/24/2001]
  Why is the term 'arc' used for the inverse of sine, cosine, and tangent, instead of just saying the function to the -1 power?

• Solve for x [Veronica, 10/26/2001]
  Solve for x over (0,2pi): 1) tan^2 x = 2sec x - 1; 2) sin x - sqrt3 cos x = 1.

• Radian to Degree Conversions [Jason, 11/11/2001]
  Can you give me a table of radian measures and their reference degree measures for the unit circle?

• Proof by First Principles [Ewart, 11/16/2001]
  How can I prove by first principles that the derivative of tan(x) is sec^2(x)?

• Sine of 36 Degrees [Steven, 11/18/2001]
  Ptolemy calculated the sine of 36 degrees geometrically using the construction of a regular pentagon. How did he do it?

• Fractions and Trig Functions [Jabbour, 11/26/2001]
  In verifying tan2x-cotx=0, if students approach the problem using (2tanx)/(1-tan^2x)=1/(tanx) they get only 4 of 6 possible solutions...

• Building a Manger [Anne, 12/03/2001]
  Given a base of 11" and two walls 7 1/2' and 6" high, both meeting the base a 90-degree angles, what is the length of the roof and what are the angle measures where the walls meet the roof?

• Trigonometry and Telescopes [Maitri, 12/15/2001]
  How is trigonometry related to how reflector and refractor telescopes work?

• Replace Sin x with 1/n [Eric, 12/19/2001]
  Solve: (5 + 2sqrt(6))^(sin x) + (5 - 2sqrt(6))^(sin x) = 2sqrt(3).

• Solving a Quartic Polynomial using a Trig Substitution [Kevin, 12/27/2001]
  I need help solving this system: y/sqrt(y^2+64) = (x+y)/25; x/sqrt(x^ 2+64) = (x+y)/20.

• Solving Trig Identities [Sarah, 12/31/2001]
  Please can you help me prove this trig. identitity: Sin X Cot X = Cos X.

• Special Angles [Patricia, 01/18/2002]
  Can you help me find the solution for theta?

• Unit Sphere [Jordan, 01/21/2002]
  Is there such thing as a "unit sphere" that has to do with trigonomic functions and the placement of points on said sphere?

• Finding a Missing Angle [Mel, 01/23/2002]
  Using trigonometry, calculate the measure of angles ABC and ACB.

• Derivation of Sum/Difference of Sine, Cosine, Tangent [Meredith, 02/16/2002]
  How can I find the derivation of the sum/difference of sine, cosine, and tangent?

• Laws of Sines and Cosines [Alison, 03/07/2002]
  When I set up the problem, the three angles don't add up to 180 degrees.

• How High is the Building? [Nancy, 03/08/2002]
  Melissa and her friends decide to fly their paper airplanes out of the window of a tall building...

• Tan pi/8 [Stepheny, 03/16/2002]
  I must find the exact value of tan pi/8.

• Cosine 20 Degrees [Matthew, 03/24/2002]
  What is the exact value of cosine 20 degrees?