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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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Finding Arc Sin [8/13/1996]

How can I use sin, cos, tan, and arctan to define arcsin and arccos?

Finding a Trig Function of an Angle [07/09/2004]

If sin(y) = 8/17, find cot(y).

Finding Coordinates [12/31/1996]

Given two intersecting line segments, the angle they form at their intersection, the coordinates of one endpoint and those of the intersection, and the length of one of the line segments, how do you determine the coordinates of the remaining endpoint?

Finding Intervals in Trig Graphs [10/25/1998]

Can you help me with graphing sine and cosine functions? How do you mark off the intervals?

Finding Shareware and Freeware for Teaching Trig [5/13/1995]

Where can I find some shareware or freeware programs for teaching trigonometry (MS-DOS, Windows, or Mac)?

Finding Sides and Angles [01/22/2001]

Can you determine the length of the hypotenuse and an acute interior angle of this right triangle?

Finding the Adjacent and Opposite Sides in a Right Triangle [06/12/2008]

What is the difference between the adjacent side and the opposite side and how do I tell which is which?

Finding the Angle of a Vector [05/10/2000]

How can I find the angle for a vector (x,y) that originates from the origin (0,0)?

Finding the Arc Length of a Hanging Catenary [07/23/1997]

A catenary is suspended between two equal poles 400 feet apart at equal height; it sags in the center 40 feet...

Finding the Area of a Regular Pentagon [04/15/1998]

How can you find the area of a regular pentagon given only the length of one side?

Finding the Length of an Arc [2/14/1996]

Find the length of an arc that subtends an angle of measure 70 degrees on a circle of diameter 15 cm., and find the area of that sector.

Finding the Period of a Squared Trig Function [08/28/2006]

How do you find the period of a cosine equation when the cosine is squared, such as y = 3 - 2cos^2[pi(x)/3]?

Finding the Third Side [04/24/1999]

Using trigonometry, how do you find a third side of a scalene triangle given two side measures and an angle measure?

Finding the Value of an Inverse Trig Function [05/08/2000]

How can I find the value of cot[sin^-1(4/5)]?

Finding Values by Hand [08/26/1998]

How can you find the exact value for sin 18, cos pi/16, etc. without using a calculator?

Finding Values of x for Trig Equation [9/11/1996]

How do I find the values of x to make: tan x = -x/((16-x^2)^.5)) true?

Finding What Number has the Sine of X [4/12/1996]

If the sine of y is x, is there a way to figure out what y is?

Find the Cities [06/19/2001]

Given the latitudes and longitudes of Detroit, MI, and Miami, FL, find every city within 10 miles of a straight line between them.

Formulas for Sine and Cosine [1/24/1996]

What are the formulas for finding sin, cos, and tan in terms of theta?

Formulas: Width, Side Length of Octagon [03/24/1997]

Given the width of an octagon, what is the length of a side, and vice-versa?

Fractions and Trig Functions [11/26/2001]

In verifying tan2x-cotx=0, if students approach the problem using (2tanx)/(1-tan^2x)=1/(tanx) they get only 4 of 6 possible solutions...

Function Frequencies [02/03/2001]

Why does the tangent function have twice the frequency of the sine and cosine functions?

General Strategy for Simplifying Trig Identities and Expressions [12/01/2003]

Simplify sin^2(x) cos^2(x) - cos^2(x).

Geometry of a Pizza [5/31/1996]

How can you divide a slice in half by cutting across a wedge?

Given a Triangle with Angles a,b,c [05/03/1999]

Show that cos(a)+cos(b)+cos(c) is less than or equal to 3/2.

Given Tangent, Find Angle [7/2/1996]

Given tan y=3n/4n, find y.

Graphing Peculiarity [07/24/2002]

When I use a calculator to graph one form of an equation it works fine; but when I use a different form, it doesn't work. What's going on?

Graphing Polar Equations [06/02/2002]

I need to graph the polar equation (r-3/5)^2 = cos(7 theta), and I don't know how to do it.

Graphing Sine and Cosine [07/07/2000]

How do you graph equations that use the sine or cosine functions?

Graphing Trig Functions [05/03/1997]

How do you graph y = 3sin4x-3?

Graphing Trig Functions [09/08/2004]

Doctor Ian's method of graphing and calibrating the axes for sine and cosine curves that involve phase shifts and period changes.

Graphing Trigonometry Equations [5/15/1996]

How do I graph this one: Sin A - Cos A ?

Graph of Circle as a Function [05/30/1998]

The graph of a circle is not a function because it fails the vertical line test. How could you make it a function?

Graph of y = arcsin x [03/31/2003]

Understanding the graph of arcsin(x).

Graphs and Gradients [05/13/2003]

Sketch graphs of f and f' for f(x) = sin x and guess the formula for f'(x).

Graphs of Sine and Cosine Functions [02/28/2003]

What is the relation between the sine and the cosine function? How is the graph of y = cos(x) linked to the graph of y = sin(x)?

Half-Angle Formula - Getting the Right Sign [06/11/2003]

Find the possible values of tan(1/2)theta when tantheta = 7/24.

The Height of a Distant Tree [07/08/1998]

If a tree is 1 mile away, and I see it as 5 cm tall, how can I find its real height?

Height of a Hill [09/06/1997]

From the top of a hill, the angles of depression of two consecutive kilometre stones due east are 30 and 45 degrees.

Height of the Plane [03/29/2001]

Towers A and B are 4.1 miles apart on level ground. A pilot finds the angles of depression to the towers to be 36.5 and 25 degrees, respectively. Find the height of the airplane.

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