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Selected answers to common questions:
Volume of a tank.
- Simplifying Trigonometric Expressions [9/13/1995]
A student asks for help simplifying and solving trigonometric
- 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
- 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
- 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?
- 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
- 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
- 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?