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High School Archive

Browse High School Trigonometry
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Selected answers to common questions:
    DeMoivre's theorem.
    Volume of a tank.

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Simplifying Trigonometric Expressions [9/13/1995]

A student asks for help simplifying and solving trigonometric expressions.

Simplify Numerator and Denominator [4/15/1996]

What is the algebra, or actually the trig that lets you simplify: - sin x + 1 / (1- sin x)^2

Simulating Sound Waves [10/27/2000]

How can I simulate a sound wave that reaches a maximum height every seventh crest?

Sine and Cosine Addition Formulas [11/29/2000]

Can you prove the addition formulas for sine and cosine? Also, if sin(2Q) = a, then what is sin(Q) + cos(Q) in terms of a?

Sine and Secant [04/30/2002]

Why isn't secant the reciprocal of sine and cosecant the reciprocal of cosine?

Sine, Cosine, and Tangent on a Circle [04/14/1999]

Where are the sine, cosine, and tangent on a unit circle?

Sine/Cosine Equations [10/23/1996]

Are there equations for sine or cosine?

Sine, Cosine, Tangent [03/13/2001]

What are sine, cosine, and tangent?

Sine, Cosine, Tangent; Four-meter Ladder [6/15/1996]

Is there any way to perform these functions without a calculator?

Sine Function and Unit Circle [08/15/2003]

Solve for x, where x is an integer: sin(pi/x) = square root2/2.

Sine numbers in Charts for Angles [12/22/1997]

I am a toolmaker and I'd like to know where the numbers in sine charts or on a calculator come from.

The Sine of 1 Degree [01/07/2001]

How can I find an exact value for the sine of 1 degree using only the values of sine for special angles and the angle-addition formulas?

Sine of 36 Degrees [11/18/2001]

Ptolemy calculated the sine of 36 degrees geometrically using the construction of a regular pentagon. How did he do it?

Sine of an Angle and Opposite Side [5/17/1996]

Given triangle ABC inscribed in a circle, prove why (sin A)/a equals the diameter of the circle.

Sines and equations [12/3/1994]

I am a tenth grade student taking AMF (advanced mathematical functions) and was given the problem: 0<=X<=150; when does the Sin 8X = Sin X? I had no problem doing this on my graphing calculator, and finding the intersects between the functions, but is there any way to do this by using some sort of equation?

Sine Series [09/09/1998]

What does sin1*sin2*sin3***sin179 equal in degrees?

Sine Squared [06/27/2003]

What is sine squared, and how do you enter it in a calculator? How do you use trig when there isn't a right triangle?

Sin of More Than 2pi, 360 Degrees [8/6/1996]

How do you find the sin of 2020?

Sin x^2, Sin^2 x, (Sinx)^2 [09/12/2001]

What is the difference between sin x^2, sin^2 x, and (sinx)^2?

Sin(x) = x? [07/01/1999]

Is it true that when x is very small (e.g. x = 10^-70), then sin(x) = x? Why?

Solution for Trig Equality [7/27/1996]

Sin x = Cos x - what does it mean?

Solve for x [10/26/2001]

Solve for x over (0,2pi): 1) tan^2 x = 2sec x - 1; 2) sin x - sqrt3 cos x = 1.

Solving and Simplifying using Trig Identities [12/5/1995]

Could you please help? 1. Solve for x: 20.0^(3x) = 85.0 2. Simplify: 1 + (sec^2(@) / cos^2(@)) 3. Show that tan^4(y) - sec^4(y) = 1 - 2sec^2(y)

Solving an Equation with Sines and Exponents [05/24/2000]

How can I solve the equation sin^2(exp(c-x)) + sin^2(exp(c+x)) = 0, where x is a (real) unknown and c is a real positive constant?

Solving a Periodic Function [3/31/1996]

Solve: sin2z = 5

Solving a Quartic Polynomial using a Trig Substitution [12/27/2001]

I need help solving this system: y/sqrt(y^2+64) = (x+y)/25; x/sqrt(x^ 2+64) = (x+y)/20.

Solving a Trig Equation [3/11/1996]

(sin (alpa))/(alpha) = ?

Solving a Trig Equation Using Sine of a Sum [08/20/2008]

How do I solve an equation like 4 cos x + 6 sin x = 5?

Solving Right Triangles [03/25/1998]

How do you know when to use sin, cos, or tan when solving right triangles?

Solving the Law of Tangents for an Angle [12/18/2004]

Given the Law of Tangents, (a - b)/(a + b) = tan (A/2 - B/2) / tan (A/2 + B/2), express angle B in terms of a, b, and A.

Solving Trig Equations with Newton's Method [06/16/2006]

How can I solve an equation like 3sin(x) = x + 1 for 0 < x < 2pi?

Solving Trig Identities [12/31/2001]

Please can you help me prove this trig. identitity: Sin X Cot X = Cos X.

Solving Trigonometric Equations in Radians [12/14/1997]

Solve for theta in radians to 2 decimals if 0 < theta < 2 pi tan theta = -0.318.

Solving Trig Problems [08/18/1997]

Find the value of Tan [(x+1)/(x-1)]^(-1) + Tan (x)^(-1).

Special Angles [01/18/2002]

Can you help me find the solution for theta?

Spiral Inside a Hexagonal Room [09/03/2003]

Two walls meet at 120 degrees, and you have a piece of cardboard with an angle of 137.5 degrees that you want to tilt until its sides are snug against the wall. How do you find the angle of tilt?

The Square Root of i [05/25/1997]

What is the square root of i?

Square Roots of Complex Numbers [03/28/1999]

Devise at least two methods for finding the square root of (a+bi).

Squares and Triangles: a Proof [8/23/1997]

Two points lie within or on the boundary of a square. Prove that the length of at least one of the lines...

Standard Angles [08/09/2001]

Why are 0, 30, 45, 60, and 90 degrees taken as standard angles in trigonometry? Why can't we take some other angles?

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