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Browse College Trigonometry
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    DeMoivre's theorem.

Limit of Perimeter/Area Ratio for Polygons [03/23/2000]
How can I show that as the number of sides of a polygon of given area increases, the perimeter of the figure decreases and the limit of the perimeter is the circumference of a circle of that given area?

Location of Plane Flying on Great Circle [11/20/2003]
An aircraft flies from 60N 030W to 60N 030W following a great circle. When 025W is passed, what will the plane's latitude be?

Mitres on Pyramids [09/26/2002]
I am weatherproofing my home, and have to mitre boards in a pyramid with a rectangular - not square - base, and an apex that is directly over the centre of one edge of the base.

Obliterating Iterating (Fazed by Phase) [10/10/2003]
Solve a*sin[theta] + b*cos[theta] = c for theta, where a, b, and c are constants. Is there a way to do this without iterating?

On the Complex Differentiability of the Hyperbolic Secant [09/24/2010]
A student wonders if sech(z) is complex differentiable, and where. Picking up on the student's familiarity with the Cauchy-Riemann equations, Doctor Jordan uses trigonometric identities to examine the function's real and imaginary parts separately, and reveals the conditions under which the function is holomorphic.

Optimization: Minimum Area [11/07/1997]
How do you fold a piece of paper (rect. with width a and unlimited length) so one corner just reaches the righthand side for minimum area?

Packing 4 Spheres Into a Tetrahedron [09/03/99]
How can I find the dimensions of the smallest tetrahedron that can serve as a container for 4 spheres packed as snugly as possible?

Parametric Form of Circle Equation [08/04/2003]
If I know the center and radius of a circle, and three points on the circle, can I find the parametric form of the circle equation in 3D space?

Phase Difference [05/30/2003]
Does the sine wave lag or lead the cosine wave by pi/2?

Proving Identity for Sum of Cosines [10/17/2003]
How do you prove the identity for the sum of cosines?

Rotation of Conics [12/01/1999]
How can I transform 17x^2 - 48xy + 31y^2 + 49 = 0 into an equation with no xy term?

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 System of Inverse Hyperbolic Trigonometry Equations ... with Natural Logs and the Quadratic Equation [03/28/2010]
Although a student struggles to solve a system of inverse hyperbolic trigonometry equations algebraically, Doctor Vogler picks up on his insight about a natural logarithm equivalence to propose a numerical solution.

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.

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?

Summation Formulas for Trigonometric Functions [04/24/2001]
How do you find the area under the curve of a trigonometric function using the definition of a limit and not an approximation? Are there summation formulas for trigonometric functions?

Sum of Sine Series [07/17/2008]
Show that for any integer n >= 1, the sum from k = 1 to n of sin(kt) is [cos(1/2t) - cos((n + 1/2)t)]/[2 sin(1/2t)].

Three Trig Problems [6/11/1996]
1) Find tan x if ((sin x)^2)/3 + ((cos x)^2)/7 = (-sin(2x)+1)/10 2) A = 20 deg. and B = 25 deg. Find the value of (1+tanA)(1+tanB). 3) Evaluate cos 36 - cos 72.

Trig Functions in Matrices [7/22/1996]
A problem involving matrices with trigonometric functions.

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

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

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

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.

Trig proof [11/30/1994]
I am a faculty member in math. I am trying to see how this Dr.Math stuff works. Here is my question. Can you show me how to prove arcsin(x)+arccos(x)=pi\2?

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.

Writing Trig Functions in x-Base [5/25/1995]
I must write trig functions (sin(), cos(), etc.) in xBase code as part of a project that I am working on (navigation bearing and distance calculations)...

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