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Selected answers to common questions:
Volume of a tank.
- Trigonometry by Hand [05/24/2002]
What formulas can I use to compute sines, cosines, tangents,
arcsines, arccosines, and arctangents without using tables or a
- Trigonometry Equations [04/23/2003]
Solve, for 0 <= theta < 360, 3cos^2(theta) - 2sin(theta) = 2, giving
solutions to 1 decimal place where appropriate.
- Trigonometry + Geometry [5/5/1996]
A right angle triangle is blocking a circle and is being blocked by
- Trigonometry Identities [01/07/1997]
Verify the identity sin(x+y+z) = sinx cosy coxz + cosx siny cosz + cosx
cosy sinz - sinx siny sinz.
- Trigonometry Identities [07/30/1997]
I have a problem with these identities...
- Trigonometry Identity [02/20/1998]
Prove a*cos(A) + b*cos(B) + c*cos(C) = 4R*sin(A)*sin(B)*sin(C).
- Trigonometry, Logs and Map Projections [10/01/1997]
I am trying to figure out the inverse function used by the Mercator map
- Trigonometry Mnemonic [04/12/1997]
How do you spell the trigonometry word that is something like SOCHOATOA?
It means side over hypotenuse, etc.
- Trigonometry Problem [8/11/1995]
A 12 metre ladder is inclined to the vertical at 48 degrees. How far is
it from the base?
- Trigonometry Proof [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)
- Trigonometry Proof [7/18/1996]
How do I prove that (cotX)(cosX)/(cotX + cosX) = (cosX)/(1 + sinX)?
- Trigonometry Proof [04/21/1997]
Prove that (sin 50 x cos 50)/tan 50 = sin^2 40.
- Trigonometry Story Problem [06/04/2002]
What angle will a shortcut make with the roads nearest it?
- Trigonometry Substitutions [09/30/1997]
I am having problems doing trig substitutions. Can you suggest any
- Trigonometry Terminology [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?
- Trigonometry Tricks [11/14/2002]
To find how (1/4)cos^4x-(1/6)cos^6x = -(1/4)sin^4x+(1/6)sin^6x, I've
tried to change all the cos to sin by using sin^2x+cos^2x = 1 and then
using double angle formulas. I am trying to prove that they are equal
to each other.
- Trigonometry Without Calculators [01/06/1997]
How do you find Cos without a calculator?
- Trigonometry Word Problem [06/05/2002]
How far did the hot-air balloon rise between observations?
- Trig Problems [05/07/1999]
What are the steps to follow in order to answer these questions? 1) cos2x
= sinx; 2) cos2x = cosx...
- Trig Problem: Sec A = -2 ... [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?
- Trig Proof - Newton's Formula [04/09/1998]
Can you prove that: (a - b)/c = sin ((1/2)(A - B))/cos ((1/2)(C))?
- Trig Proof: Two Methods [03/26/1998]
Prove: (1 + sin x + cos x)/(1 - sin x + cos x) = (1 + sin x)/cos x.
- Trig Ratios of a Right Angle in a Right Triangle [09/21/2006]
I'm learning about trig ratios in terms of the hypotenuse, opposite,
and adjacent sides of a right triangle. I'm wondering how those sides
apply to the right angle? Is the hypotenuse the opposite? What's the
- Trig Word Problem [5/5/1996]
Find the height of the tower...
- Trisected Hypotenuse of a Triangle [12/20/1998]
In right triangle ABC, with C as the right angle... what is the length of
AB (the hypotenuse)?
- The Troublesome Endpoints of a Trigonometric Series [04/10/2011]
A student has doubts about the radius of convergence assumed in a proof that
involves integrating a power series. Doctor Vogler confirms his suspicion about the
behavior of endpoints of integrated series, and introduces Abel's Theorem.
- Tutorial material/books/help [11/16/1998]
Can you suggest something I can order or download to help me with
trigonometry and pre-calculus?
- Two Airplanes [08/28/1997]
Draw a diagram using coordinate system with origin O - how far apart are
the airplanes? Express the answer in radical form.
- Two Dogs Pulling a Sled [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
- Two Problems on Tangents [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...
- Two Slopes, and Two Ways to Average Them [01/06/2016]
An adult has questions about the validity of a colleague's simple
method to average slopes — and about simplifying his own, more
involved approach. With sketches, trigonometric identities, and
conjugate products, Doctor Peterson explains the methods, and shows
- Two Triangle Problems [6/11/1996]
One angle of a triangle is trisected... Find the shortest side.
- Two Trigonometry Questions [1/22/1995]
What is sin60 * cos60, and tan45 * tan3?
- Understanding Bearings in Directional Problems [01/14/2004]
A boat sails 10km from a harbor H on a bearing of S30 degree E. It
then sails 15 km on a bearing of N20 degree E. How far is the boat
from H? What is the bearing from H?
- Unit Sphere [01/21/2002]
Is there such thing as a "unit sphere" that has to do with trigonometric
functions and the placement of points on said sphere?
- Usefulness of De Moivre's Theorem [2/10/1996]
What is the usefulness of de Moivre's theorem?
- Using Forth to Find asin(x) or acos(x) [03/16/2004]
I am writing a program in Forth. I have available tan, atan, cos and
sin. I have three sides of an oblique triangle. How can I find the
angles? I know I can do it if I have asin. Is there another way, or
can I define asin in terms of what I have available?
- Using Graphs of Trigonometric Functions [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?
- Using Newton's Method to Solve an Implicit Equation [10/14/2007]
How can I solve the equation (sin(X))/X = 0.7031? My book gives the
answer but does not explain how to find it.
- Using Phase Shifts to Modify a Sine Curve [06/30/2005]
What modifiers can be used to fatten a sine wave while not affecting
the zeros and peaks?