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Trigonometry

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

Selected answers to common questions:
    DeMoivre's theorem.
    Volume of a tank.



Averaging Two Angles [06/08/1999]
How do you take the average of two or more angles?

Basics of Trigonometry [12/12/2001]
Why is trigonometry important? How is it used in the real world?

Calculating Height in the Air [11/14/2001]
I need to know the formula for calculating the height of an object, like how high in the air an object is.

Carrying a Ladder around a Corner [02/28/2003]
A ladder of length L is carried horizontally around a corner from a hall 3 feet wide into a hall 4 feet wide. What is the length of the ladder?

Changing a Trigonometric Graph [08/06/1998]
How do you graph: -cos 2x / 2?

Curious Property of a Regular Heptagon [04/06/2001]
How can I prove that in a regular heptagon ABCDEFG, (1/AB)=(1/AC)+(1/ AD)?

Defining the Six Trigonometric Functions on the Unit Circle [09/11/2003]
I can find sin, cos, and tan on the unit circle, but I don't know how to find csc, cot, and sec.

Deriving Sines of 30, 45, 60 and 90 Degrees [06/02/1999]
Where do the values for sin 30, sin 60, etc. come from?

Deriving the Dot Product [09/17/1998]
Can you explain how to derive the formula for the dot product?

Explanation of Sine and Cosine [7/30/1996]
I am having trouble with the topics of sine and cosine.

Find Angle Given 3 Sides, NOT Using Law of Cosines [12/18/2001]
Why doesn't it work to use proportions?

Flying a Kite [5/23/1996]
Find the angle of elevation of a kite...

Geometry vs. Trigonometry [07/14/1997]
What is the difference between trigonometry and geometry?

History and Uses of Trigonometry [9/10/1995]
What is trigonometry?

Latin Origins of Trig Functions [11/20/1998]
What are the etymologies of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent?

Proving Identities Rigorously [01/23/2002]
I've been taught that the proper way to work on identities is to work with one side at a time only.

Pythagorean Theorem and non-Right Triangles [03/09/2002]
Why doesn't the Pythagorean theorem work for triangles other than right triangles?

Sine and Cosine Without a Calculator [9/2/1996]
How do I find sines and cosines without using a calculator?

Sine, Co-sine, and Tangent: SOHCAHTOA [03/28/1999]
I am having trouble figuring out what to use when solving a triangle problem.

Techniques of Integration - Change of Variables [02/17/1999]
Solve: (integral sign) sin 2x/ sq rt (9-cos^4 x) dx .

Trig Identities [11/5/1994]
I am a junior in High School and currently taking a pre-calc. course. We started the year with trig. identities. What confuses me is how to find the exact value (i.e, not a decimal answer) of an angle (in radians or degrees) QUICKLY. For several of our problems we need to know almost instantaneously the value of say, sec 15, sin 45, cos 60, etc. Instead of drawing a triangle on a cartesian plane and using the 30x30x60 or 45x45x90 rules, is there an easier way to derive the answers to these questions quickly?

Trigonometric Functions and the Unit Circle [05/22/2000]
Why don't sine and cosine graphs have values greater than 1 or less than -1? Why does the tangent graph have asymptotes? How do the trig functions relate to the unit circle?

Trigonometric Identities [11/13/1997]
Do you have any suggestions for finding an easy way to remember them that I could apply to all identities?

Trigonometry in a Nutshell [04/11/2001]
What is trigonometry? Can you give me some problems and examples? What does trigonometry have to do with circles? with waves?

Trigonometry: Positive vs. Negative [5/31/1996]
The problem: tan x = 5/12 and sec x = -13/12

The Unit Circle [4/2/1996]
Could you describe how to "read" the unit circle?

Volume of a Cylindrical Tank [2/3/1995]
I have to keep an inventory of how much is kept in a farm of tanks outside my school. The tanks are cylindrical, which would be no problem if they were standing on end...

What is Arctan? [8/28/1996]
For the function f(x) = sin (arctan x), is sin the same as arctan X?

Why Sine, Cosine, and Tangent? [11/29/2001]
Why does sine equal opp/hyp, cos equal adj/hyp, and tan equal adj/opp?

30-60-90 and 45-45-90 Triangles [03/15/1999]
If I have a triangle that is 30-60-90 or 45-45-90, how do I find all the sides when given only one side? Where does trigonometry come in?

Algebra and Trig Equation [4/20/1996]
How can I solve this equation: 1 = sin(3x) - cos(6x) ?

Algebraic Expression for cos(arctan(x)/3) [8/15/1996]
How do I find an algebraic expression for cos(arctan(x)/3) so that I can get rid of the trigonometric operands?

Altitude of a Model Rocket [10/26/1999]
I need an algebraic formula that determines the altitude of a rocket based upon inclination observations of three ground observers.

The Ambiguous Case [04/01/2003]
How many triangles can be constructed if, for example, a=4, A=30, and c=12? Or a=9, b=12, and A=35?

Ambiguous Cases - Laws of Cosines and Sines [04/26/2000]
When I try to use the law of cosines and the law of sines on triangle ABC, with sides of length a = 3.2, b = 4.3 and c = 5.1, I get two different answers.

Amplitude of Function with Sine and Cosine [01/11/2004]
How do you predict the amplitude of a function involving both sine and cosine? For instance, how is it possible to find the amplitude of f(x) = a*sin(x) + b*cos(x) without using an automatic grapher?

Angle Between Two Sides of a Pyramid [10/29/1999]
How can I compute the angle formed by two sides of a frustrum of a pyramid?

Angle of Elevation [01/22/1997]
A tree 66 meters high casts a 44-meter shadow. Find the angle of elevation of the sun.

Angle of Sun's Rays [05/03/1999]
How can you determine the angle at which the sun's light hits the earth at any given point?

Angle, Side Length of a Triangle [9/4/1996]
What is the relation between the angles and side lengths of a triangle?

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