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Selected answers to common questions:
Volume of a tank.
- Steiner-Lehmus Theorem [01/28/1999]
I have a proof about an isosceles triangle that I just can't figure
- Strategies for Proving Trigonometric Identities [05/19/2003]
How can I prove the identity (1-sin)/(1+sin) = tan + 1/cos?
- Substituting to Simplify the Integral [08/04/2003]
What is the integral of tan^3 x * secx dx?
- Subtracting and Multiplying Sines of Angle Multiples [04/01/2010]
Using the trig identity for the difference of sines, Doctor Jacques helps a student prove
the equivalence of two trigonometric expressions involving angles that happen to be
multiples of each other.
- Subtraction of Trig Functions with a Phase Shift [09/14/2004]
How do you find the difference between two trigonometric functions
with the same frequency, but one is phase shifted by 120 degrees?
- 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)].
- Surface Area of a Cone [06/18/1998]
What is the formula for the surface area of a cone?
- Surface Area of an Oblate Spheroid [06/02/1999]
Could you please give an example of solving for the surface area of an
oblate spheroid using the inverse hyperbolic sine function?
- Tan 90 [07/10/1998]
Why is tan 90 undefined?
- Tan, Cos, Sin [05/21/1999]
Please tell me about tan, sin, and cos. How do you know which one to use?
- Tangent [02/14/2003]
Is the trigonometric ratio tangent related to the tangent of a circle?
- Tangent and Secant [2/2/1995]
I need help with the following problem: tan b + cot b = sec b csc b
- Tangent Function and the Unit Circle [06/06/2002]
When demonstrating the tangent function on the unit circle, why does
the picture 'flip' when the angle passes through pi/2?
- Tangent of 90 Degrees [5/24/1996]
Why is the tangent of 90 degrees undefined?
- Tangent to Graph of y = e^x [10/09/2003]
On the graph of y = e^x is point Q with coordinates (b,a). The tangent
to Q makes an angle x with the x-axis. Why is it that tan(x) = a?
- Tan pi/8 [03/16/2002]
I must find the exact value of tan pi/8.
- Terminal Side [04/21/1997]
Find cos(A) if the point (2,-3) is on the terminal side of A.
- 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.
- The Top of the Tower [07/20/2001]
Given a 300-mile-tall tower on the earth, how far away from it can you go
before the top disappears below the horizon?
- Train in the Rain [11/21/1996]
Given a train moving in the rain, determine the actual velocity and
direction of the raindrops/the train from how raindrops appear on the
- Transforming Trig Functions [05/08/2001]
Express 3 sin x + 5 cos x in terms of sin x so that the graph is the same
as the first equation.
- Translating Trig to Algebra; Proving Trig Identities [08/09/2002]
Write as algebraic expressions in x, free of trig or inverse trig
functions: sin(arccos x), tan(arcsin x), cos(arccot x), sec(arctan(x+
2)). Prove these identities: sec^2 x + csc^2 x = sec^2 x (csc^2 x);
sin^4 x + 2sin^2 x (cos^2 x) +cos^4 x = 1.
- Triangles and Law of Sines [03/27/1998]
How can you use the Law of Sines to produce more than one triangle?
- Triangular Garden [03/18/1997]
Find the length of a fence that runs from the right angle to the
hypotenuse and separates the garden into two parts of equal perimeter.
- Trig and Inverse Trig Problems [7/30/1995]
I have three trig-related questions. Would it be possible to include
explanations for solutions and some general rules?
- Trig Based on the Unit Square [10/22/1998]
Why are the sine and cosine graphs defined in a unit circle? Why not a
unit square or any other geometric shape?
- Trig Equation [6/22/1996]
Solve for x: (cos(x))^2+(sin(x))^2 = (15*(cos(x))^2)/18)-(1/2)
- Trig Function Domains [08/23/1999]
Which came first, trigonometry based on the simple triangle or
trigonometry based on the triangle of the unit circle?
- Trig functions [11/22/1994]
What is the definition of sine, and the other trig functions? I
understand how to get it, but why was it chosen to be like that? How come
all triangles have this property? Does it have something to do with the
fact they all have 180 degrees?
- Trig Functions [9/29/1996]
How do you know when to use sine, cosine, and tangent?
- Trig Functions in Forth [04/07/2003]
I am writing a program in the language Forth. I need to determine the
two missing angles in a right triangle...
- Trig Functions in Three Problems: Graphing, Solving, and Factoring [05/15/1998]
Graphing sin(x) - cos(x), solving sqrt(3)*cos(x) = sin(x), and factoring.
- Trig Functions of Angles Expressed in Degrees and Minutes [05/04/1998]
Using calculators to evaluate trigonometry functions of angles expressed
in degrees and minutes.
- Trig Functions, Reference Angles, and the Unit Circle [07/02/2004]
A discussion using the unit circle to show why sin(A) = sin(180 - A)
and introducing other similar identities based on reference angles.
- Trig Identities [04/16/1999]
I have to prove that cos 36 (or sin 54) = (1+sqrt(5))/4.
- Trig Identities and Double Angles [01/04/1998]
Prove that sec2A + tan2A = cosA + sinA / cosA - sinA.
- Trig Identities Simplify a Challenging Integration [02/11/2005]
How would you integrate 1/[asin(theta) + bcos(theta)]^2 ?
- Trig Inverses: sin(arctan x) [11/04/2002]
We discussed inverses of trig functions, but when the teacher added an
x, I didn't understand.
- Trignometric Functions [5/31/1996]
I have to find the four missing trig functions...