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Selected answers to common questions:
Volume of a tank.
- Proof of a Trig Identity [03/13/1998]
Proving that (1 + sinX + cosX)/(1 + sinX - cosX) = (1 + cosX)/sinX.
- Proof of DeMoivre's Theorem [05/01/1997]
A typical induction proof: DeMoivre's theorem.
- Proof of the Parallelogram Law [08/07/1999]
How do you prove the parallelogram law geometrically, without using
- Proof of Trig Identity [7/24/1996]
Prove (sin 2t + sin t)/(cos 2t + cos t + 1) = tan t is an identity.
- Proving a Trigonometric Identity [06/06/1999]
How can I prove the trigonometric identities cos(a+b)*cos(a-b) = cos^2a -
sin^2b, and tan(x/2) = (1-cosx)/(sinx)?
- Proving a Trigonometry Identity [05/19/2003]
Prove the following identity: cos 3x = 4 cos^3x - 3cosx.
- Proving De Moivre's Theorem [12/03/1997]
Prove De Moivres theorem: - (cos(x)+isin(x))^n = cos(nx) + isin(nx) .
- Proving Identity for Sum of Cosines [10/17/2003]
How do you prove the identity for the sum of cosines?
- Proving Laws of Sines, Cosines [10/01/2003]
How do you prove the laws of sines and cosines?
- Proving Sine Identities [05/16/1998]
Can you help me prove the trigonometric identities for sin(A+B), sin(2A),
- Proving Trig Identities [11/15/1998]
How do I prove trig identities like sin^6x+cos^6x = 1-3sin^2xcos^2x?
- Proving Trig Identities vs. Solving Trig Equations [10/08/2006]
Proving the identity sinx/(1-cosx) - (1+cosx)/sinx = 0 is done a
little differently than solving that same equation for x, though the
thinking is very similar. What is the key to proving the identity?
- Proving Trigonometric Identities [02/12/1999]
Tips on proving trigonometric identities, as well as a good general
procedure to use, worked out on cos^4(x) - sin^4(x) = cos(2*x).
- Proving Trigonometry Identities [01/07/1997]
Prove these trigonometry identities (tan x+cot x)tan x = sec^2 x and
(1+cos x)(1-cos x) = sin^2 x
- Pythagorean and Other Triangle Theorems [1/6/1995]
Could you please show me the proof for the Pythagorean Theorem and list
the other triangle theorems that are based on it?
- The Pythagorean Identity for Cosine [11/11/1995]
If Sin 9 = x , what is the solution and result of Cos9.cos18.cos36?
- Pythagorean Identity of Trigonometry [02/16/1998]
Proof of the trigonometry identity sin^2 + cos^2 = 1.
- Radians [03/22/2001]
I have searched everywhere for the history behind radians. Why did they
- Radian to Degree Conversions [11/11/2001]
Can you give me a table of radian measures and their reference degree
measures for the unit circle?
- Radius of Circumscribed Circle [05/11/2001]
Where can I find a derivation of R = abc/4K?
- Rail Bend in Hot Weather [10/13/2002]
A 20-ft piece of rail expands 1 in. in length during a hot spell. If
there are no expansion gaps, how high off the ground will the rail
- Raised Cosines [01/28/2001]
What are raised cosines, and how do they work?
- Ratios, Geometry, Trigonometry [06/10/1999]
A homeschool teacher asks for help with triangles, flagpoles, and
- Rearranging x=tan()sin() [05/01/2002]
How would I approach rearranging x = tan(y)*sin(y) into y = some
function of x?
- Reflections in Parabolic Mirrors [05/14/2005]
I know that in a parbola, any ray that starts at the focus and hits
the parabola is reflected parallel to the central axis of the
parabola. Can you explain or prove why that happens?
- Related Rates - Clock Hands [04/05/1999]
How fast is the distance between the tips of the hands on a watch
changing at one o'clock?
- Remembering Trig Functions [09/27/2001]
We have to memorize the sine, cosine, tangent, secant, cosecant, and
cotangent for 30, 45, and 60 degrees for precalculus class. Do you have
any tips on how to remember these?
- Replace Sin x with 1/n [12/19/2001]
Solve: (5 + 2sqrt(6))^(sin x) + (5 - 2sqrt(6))^(sin x) = 2sqrt(3).
- Right Triangle Kite Problem [01/16/1997]
When flying a kite, 150 ft. makes an an angle of 51 degrees with the
ground. Assume the string is straight; how is the kite?
- Right Triangle Sides [09/14/1998]
To use SOHCOHTOA, I need help finding which sides are opposite and
- Roots of a Complex Equation [04/28/1997]
Given that cos t + isin t is the root of z^3 + az + b = 0 in which sin t
is not equal to 0, and that a and b are real and not equal to zero, show
that a + b^2 = 1.
- Rotating a Point around an Angle [05/16/1997]
How do you derive the formulas for rotating a point around an angle?
- Scaling a Right Triangle [12/01/2003]
Start with a right triangle of known dimensions. Move the hypotenuse
by some distance towards the right angle. What are the dimensions of
the new triangle?
- Secant, Cosecant, and Cotangent [01/16/1997]
How do you understand the secant, cosecant, and cotangent functions?
- Shadow Moving Along a Wall [08/16/1999]
There is a light at the front of a circular arena. A boy starting from B
runs at the rate of 3 m/s toward the center C. At what rate will his
shadow be moving along the rear wall when he is halfway from B to C?
- The Shortest Crease [12/29/1997]
A piece of paper is 6 units one side and 25 units on another side...
- Shot Out of a Cannon [10/12/1998]
A performer is shot out of a cannon at 30 degrees from the horizontal, to
land 20 meters away... What should his initial speed be?
- Signs of Sines (and Other Trigonometric Ratios) [07/11/2002]
The trigonometric ratios have the signs + or -, depending on the
quadrant. How do you know which signs to use in which quadrants?
- Simplifying Circle Formulas from the Dr. Math FAQ [04/30/2004]
In your FAQ on circle formulas, in the sections where the other five
values are derived from any two known values, could you write each
formula in terms of only the two known values, instead of using the
- Simplifying Expressions with Double-Angle Formulas [05/25/1998]
Using double-angle formulas, can you help me express 1 - 2*sin^2(4x) and
2*sin(5x)*cos(5x) as a single function?