Ask Dr. Math High School Archive

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 TOPICS This page:   trigonometry    Search   Dr. Math See also the Dr. Math FAQ:   trigonometry formulas See also the Internet Library:   trigonometry HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Trigonometry Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     DeMoivre's theorem.     Volume of a tank. Deriving Identities [08/26/1998] I'm supposed to derive the identity for sin 3x in terms of sin x. Deriving the Arcsin Formula [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)? Deriving the Coordinates of the pi/6 Family [06/09/1999] How do you derive the coordinates of the pi/6 family on the unit circle, and why does this work? Deriving the Haversine Formula [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. Deriving the Law of Cosines [04/01/1998] Will the Pythagorean Theorem work with a non-right triangle? Deriving Trig Functions; Taylor Series [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? Deriving Trilinear Coordinates [05/18/1999] How do you derive the trilinear coordinates of the orthocenter of a triangle? Determine Flagpole Height without Access to the Pole [12/01/2003] I need to find the height of a flagpole, but am not allowed within 10 feet of the pole. I can't measure the 10 foot limit, which makes accurate measurement of the pole's shadow impossible. How do I do it? Determining an Angle From Side Views [07/24/2002] In the end elevation of a drawing, a rod rises from point A at 32 degrees. In the side elevation, the same rod is seen rising from point A at 48 degrees. How do I work out at what angle to cut the end of the rod? Determining Measure of Angle Without Tables or Calculators [03/05/1998] Arctangent formula for determining measure of angle XOP, given P(x,y) on the unit circle. Determining Triangle Similarity [05/26/1998] Given two triangles, how can you determine if they are similar? Diameter of the Base of a Cone [08/12/1998] How do you find the formula to calculate the diameter of the base of a cone of nine degrees at various lengths? Difference Between arsinh and arcsinh Functions [05/13/2004] Why isn't there a "c" in arsinh, arcosh, and artanh? These are the equivalents of arcsin, arccos and arctan but they are hyperbolic. Different Answers with Sine Rule and Cosine Rule [08/07/2002] Triangle ABC has measurements AB=8.2cm, BC=9.4cm and AC=12.8cm and angle A=47 degrees. Find angle B. Why does using the Sine Rule here fail to give the right answer? Differing Definitions of arcsec(x) Lead to Confusion over Signs [12/03/2005] I was trying to prove the derivative of arcsec(x), and according to my book sec(arcsec x) equals |x|, but I think it should just be x. Can you explain what I'm missing? Distance from A to B [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. Domain of Arccot [05/23/2002] Why is the arccot function defined over 0 to pi, rather than from -pi/2 to pi/2? Double- and Half-Angle Identities [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). Double and Half-Angle Identities [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? Drawing an Arrow [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. Equations for Cartesian and Polar Coordinate Conversions [05/06/2003] Given the following points in polar coordinates, find the rectangular coordinates. (22, 51 degrees) Equations for the Paths of Four Lady Bugs [12/02/1998] Four ladybugs travel from the corners of a square towards the center. Find the equations that describe the path. Equilateral Triangle: Area Formula and Proof [06/16/1998] Is there a formula to find the area of an equilateral triangle given a point on its interior and the lengths of the segments from the point to the three vertices? Etymologies of Algebra, Geometry, Trigonometry [10/22/2001] What are the origins and roots of the words geometry, algebra, and trigonometry? Etymology of Cosine [5/21/1996] Where does cosine come from? Euler Equation [01/21/1997] What is the meaning behind e^(pi*i) = -1? Euler Equation [09/13/1997] Does the Euler equation still work if we decide to work in degrees? Is it arbitrary? Euler's Theorem [05/09/2003] Solve: sine(x) = 2. Evaluating a Trigonometric Expression [07/31/1999] Can you help me evaluate tan (arcsin (3/5))? The Exact Value of the Sine of 1 Degree [05/24/2000] Has anyone ever figured out the exact value for the sine of 1 degree or pi/180 radians? Explaining How SohCahToa Works [07/26/2004] Can you please explain what "sohcahtoa" is all about so that I can understand it? I'd really appreciate it. Explaining the Dot Product [04/05/1998] Exactly what does the dot product represent? Expressing Arccos in Terms of Arctan [02/24/1997] How do you express Arccos in terms of Arctan? Extraneous Roots Introduced Trigonometrically [06/10/2012] A student wonders what introduces extraneous roots into trigonometric identities and problems. Doctor Peterson disentangles the root causes, and offers some remedies. Factoring: cos^3t + cos2t + sin^3 t = 0 [04/23/2003] How can this expression equal 0? I need to find ALL solutions between 0 and pi. Factoring with Trigonometry [3/5/1996] 4tan^2X + 7tanX - 2 = 0 Ferris Wheel [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? Find a Function, Integrals [12/17/1997] Suppose the graph of f has the formula f(x)=-x+1 for 0<=x<=1; x-1 for 1]

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