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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.

Trekkie Trig [08/13/2013]
To find a Starship U.S.S. Enterprise Constitution Class ship's distance to another object in outer space, Doctor Jeremiah uses angles of view and stereo photogrammetry.

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

A Triangle Vertex Bisection and Its Trio of New Lengths [06/08/2012]
A trigonometry student struggles to express where the bisector of a triangle vertex intersects the side opposite it; and to describe the bisector's length in terms of the triangle's side lengths and angle measures. Doctor Peterson unpacks formulas for both, along the way invoking the Law of Cosines — and another doctor's prior work.

Triangular Garden [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.

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

Trig Based on the Unit Square [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?

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

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

Trig functions [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?

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

Trig Functions in Forth [04/07/2003]
I am writing a program in the language Forth. I need to determine the two missing angles in a right triangle...

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

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

Trig Functions, Reference Angles, and the Unit Circle [07/02/2004]
A discussion using the unit circle to show why sin(A) = sin(180 - A) and introducing other similar identities based on reference angles.

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

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

Trig Identities Simplify a Challenging Integration [02/11/2005]
How would you integrate 1/[asin(theta) + bcos(theta)]^2 ?

Trig in the Age of Calculators, and Why Don't We Just Measure the Triangles Directly? [01/10/2015]
A teen wonders about the purpose of trigonometric functions. Don't they just represent sidelengths of triangles that we could already measure, and even more immediately evaluate with a calculator? With a few historical asides, Doctor Peterson unpacks definitions.

Trig Inverses: sin(arctan x) [11/04/2002]
We discussed inverses of trig functions, but when the teacher added an x, I didn't understand.

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

Trigonemetric Identities [02/11/2003]
I'm struggling with the concepts of compound angle formulas, products of sums or differences, and multiple and half angles. Is there a connection between these and all the trig identities?

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

Trigonometric Equation for a Sequence [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.

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

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

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

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

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

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

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

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

Trigonometric Proofs [09/13/2004]
How do I prove that (sinA - sinB)/(cos A + cosB) = tan(A/2 - B/2)?

Trigonometry -- Airport Word Problems [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...

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

Trigonometry and Music [12/21/1998]
How is trigonometry used in music?

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

Trigonometry and Space Exploration [05/29/2002]
How does Trigonometry relate to space exploration?

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

Trigonometry and the Chain Rule [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?

Trigonometry and the Earth [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?

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