See also the
Dr. Math FAQ:
See also the
Browse High School Trigonometry
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Volume of a tank.
- 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 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?
- Using Sine and Tangent to Find Pi [08/01/1998]
How can I determine the sine or tangent of an angle without using a
- Using Slopes to Find the Angle between Lines [11/02/2005]
What is the formula to find the acute angle between two intersecting
- Using the Law of Cosines [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.
- Using the Law of Cosines [05/21/1998]
Given the length of three sides of a triangle, how can I find the angle
between any two of the sides?
- Using the Laws of Sine and Cosine [9/24/1995]
How do I find the sine and cosine of pi/12?
- Using Trig Identities to Simplify [7/26/1996]
How do I simplify ((sin @ - 1)/cos @) - (cos @/(sin @ -1)) ?
- Using Trigonometric Identities [05/31/1999]
How can I prove that sin(4x) = 2sin(2x) - 8sin^3(x)cosx ?
- Value of Angle DBC [1/23/1996]
Imagine a triangle ABC on which angles B and C are equal to 80...
- Vector Angles: Prove A.B = |A||B|cosA [07/13/1998]
I just finished my pre-calc class, and at the end we covered vectors...
- Verifying Trigonometric Identities [07/12/2002]
How do you verify a trigonometric identity?
- Verify the Identity [04/17/2003]
Verify the identity: (csc x)/(tan x + cot x) = cos x.