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High School Archive

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.

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Circle and Rectangle Area Problem [11/03/2003]

One corner of a rectangle is on the center of a circle. The radius is larger than the small side of the rectangle but smaller than the large side. What is the area of their intersection?

Circle of Radius 1 km around Given Latitude/Longitude [08/27/2002]

I need feed points for a circle of radius 1 km with center at a given latitude and longitude. Eight or more points should be enough for the program.

Circle on a Sphere Equation [05/05/2000]

How can I find an equation for all points that fall within a given radius from a single latitude and longitude on the surface of a sphere?

Circular Motion [01/27/2001]

Two problems: An electric hoist is being used to lift a piece of equipment... A car is moving at a rate of 50 miles per hour and the diameter of its wheels is 2.5 feet...

Circumference at a Given Latitude [01/26/2001]

How can I calculate the circumference of a line around the earth (a circle) at 40 degrees north latitude?

Circumference of a Globe [1/27/1996]

How do you derive a formula to find the circumference of a large globe hung 25 feet in the air?

Classifying Sides of a Right Triangle [06/12/2002]

How do you find the adjacent side, opposite side, and hypotenuse of a triangle?

Co-functions and Solving Trig Equations [11/18/2004]

If sin(3x - 26)° = cos(5x - 60)°, find x.

The Collapse of Compasses that Do Not Copy Segments, and the Lengths We Go To [04/16/2011]

A teacher wonders, "Since when do collapsible compasses copy lengths?" Suggesting that Euclid may have posited this basic ability early among his propositions -- for the purposes of simplifying more interesting constructions -- Doctor Peterson then goes on to discuss the pedagogical pros and cons of compass quality, reliance, and over-reliance.

Common Mistake in Simplifying Trig Expressions [12/07/2003]

I don't know how to simplify this problem: (sin^2(x) - cos^2(x)) / (sin^2(x) - sin(x)cos(x))

Complex Numbers and Trigonometry [12/25/1996]

If x is a real number, ArcSin(Sin(x)) = x. If z is a complex number, ArcSin(Sin(z)) does not equal z. Why?

Complex Numbers, Trig Functions and Roots of 1 [10/30/1997]

I'm convinced that, for an arc of length x in radians: (cos x + i sin x)^(2 pi / x) = 1... It's cool but why does it work?

Computers and Trigonometric Functions [02/11/1997]

How do computers and calculators calculate values for sine, cosine, and tangent?

Computing Angles of a Right Triangle [09/04/1997]

Is there a way to compute the other two angles of a right triangle without a calculator? If a table is required, where can I find it?

Computing Sine and Cosine [8/27/1995]

Is it possible to compute sine and cosine for a given angle without using a calculator or a sine table?

Computing sin without a Chart [02/23/1998]

Is there a formula for converting a sin angle back to degrees?

Continued Fraction for Tan(x) [11/03/2000]

Can you tell me why the "infinite continued fraction representation" for the tangent function works?

Convergence of Product of Sines [10/17/2003]

Prove that (sin(pi/n))*(sin(2pi/n))*...*(sin((n-1)pi/n)) = n/(2^(n-1)) for n >= 2.

Cosine 20 Degrees [03/24/2002]

What is the exact value of cosine 20 degrees?

Cosine Addition Formula [12/13/1997]

How can you prove the addition formula for cosine by using right triangles?

Cosine Approximations [12/29/1997]

You derived a cubic equation for cosine of 40 degrees - did you know this approximation...?

Cosines and Sines [6/16/1996]

Why does cos A = sin (90 - A)?

Cosines of Three Angles [05/08/2003]

Show that the largest angle of the triangle whose sides are 4, 5, and 6 is exactly twice the size of the smallest angle.

Covariants [05/02/1997]

Express tan(pi/2 + X) as a single function of X or as a constant.

Crossing a Canyon [5/10/1995]

Basically, we're trying to cross a canyon. From a point on one side, a rope stretches across and drops ten feet vertically...

Curious Composition a Matter of Degrees [02/18/2011]

A student wonders about the curiously consistent output of a composition of trigonometric functions. Examining the range of the tangent, sine, and cosine functions, Doctor Peterson unravels the mystery.

Cycloids [06/16/1998]

What are cycloids, and how do they differ from sine curves?

Defining the Arcsinh Function [08/09/2003]

Find an exact value for x in: 4 sinh x = 3

Defining the Complement of an Angle [08/04/2007]

If the complement of x is 90 - x, the complement is negative for x greater than 90. I've seen conflicting definitions of the complement, some saying it cannot be negative and others placing no restrictions. Which is correct?

Definition of a Tangent [10/27/1995]

What is the tangent of an angle?

Degree Measure of a Central Angle [07/29/1997]

Find the degree measure, to the nearest tenth, of a central angle whose intercepted arc measures 21 cm. in a circle of radius 4 cm.

Degrees, Minutes, Seconds [08/26/1997]

I know that degrees are what you use to measure angles, but I thought minutes and seconds were time measurements...

DeMoivre's Formula [08/13/1998]

Can you explain DeMoivre's Theorem?

de Moivre's Formula [08/11/2002]

How do I use de Moivre's formula to express cos(3p) and sin(3p) in terms of cos p and sin p? And why would this be useful?

Demonstrating Sin, Cos, Tan on the Unit Circle [12/30/1998]

Can you recommend a good way to demonstrate the trig functions sine, cosine, and tangent? What about on the unit circle?

Derivation of Law of Sines and Cosines [11/02/1997]

How do you derive the law of sines and the law of cosines?

Derivation of Sum/Difference of Sine, Cosine, Tangent [02/16/2002]

How can I find the derivation of the sum/difference of sine, cosine, and tangent?

Derivations of Heron's Formula [11/24/1998]

How is Heron's formula (Hero's formula) derived?

Deriving a Trig Identity [04/09/1998]

Can you derive the identity tan(x)+tan(y)+tan(z) = tan(x)tan(y)tan(z), where x, y, and z are angles of a triangle?

Deriving Identities [08/26/1998]

I'm supposed to derive the identity for sin 3x in terms of sin x.

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