These two functions form the foundation of trigonometry.

If t is an angle in standard position whose terminal side intersects the unit circle at point
P= ( x,y ) as shown in the diagram, then sin of t - abbreviated sin(t) or sin t - is the y-coordinate of that point, and cosine of t - abbreviated cos(t) or cos t - is the x-coordinate. In other words P = ( x,y ) = ( cos(t), sin(t) ).

Sine and cosine are called trigonometric functions.

If P is the point where the unit circle meets the terminal side of an angle of t degrees, then the y-coordinate of P is the number sin(t). We can get a rough idea of the values of the graph of f(t) = sin(t) by watching the angle t and the y-coordinate of P as the point P moves on the unit circle in the first quadrant in the animated picture below.ÝClick here to start the movie, then click the BACK button to get back to this page.Ý On the movie page, double click anywhere on the page to start the animation and click once anywhere on the page to stop the movie.
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a) What is the value of :
Ýsin(0) = ? , sin(90) = ? , sin(180) = ? , sin(270) = ? , sin(360) = ? , sin(450) = ?,
 sin(-90) = ?, sin(-180) = ?, sin(-270) = ?, sin(-360) = ? sin(45) = ?

b) What is the domain of f(t) = sin(t) ?
ÝÝWhat is the range of f(t) = sin(t) ?

Answers : a) 0, 1, 0, -1, 0, 1, -1, 0, 1, 0, 0.7071

ÝÝÝÝÝÝÝÝ b) Domain: All real numbers. Range: [ -1, 1]

To see what the graph of f(t) = sin(t) looks like click here, then click the back button to get back to this page.

If P is the point where the unit circle meets the terminal side of an angle of t degrees, then the x-coordinate of P is the number cos(t). We can get a rough idea of the values of the graph of f(t) = cos(t) by watching the angle t and the x-coordinate of P as the point P moves on the unit circle in the first quadrant in the animated picture below.Ý Click here to start the movie, then click the BACK button to get back to this page.ÝOn the movie page, double click anywhere on the page to start the animation and click once anywhere on the page to stop the movie.Ý
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b) What is the domain of f(t) = cos(t) ?
ÝÝWhat is the range of f(t) = cos(t) ?

Answers : a) 1, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0.7071

b) Domain: All real numbers. Range: [ -1, 1]

To see what the graph of f(t) = cos(t) looks like click here, then click the back button to get back to this page.
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