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Dr. Math FAQ:
Browse College Trigonometry
Stars indicate particularly interesting answers or
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Selected answers to common questions:
- 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 60°N 030°W to 60°N 030°W following a great
circle. When 025°W 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
- 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
- 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