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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.
 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
calculator?
 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
another circle...
 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
projection.
 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
methods?
 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[40] without a calculator?
 Trigonometry Word Problem [06/05/2002]

How far did the hotair 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
adjacent?
 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 precalculus?
 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
constant velocity?
 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
their equivalence.
 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?
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