CALCULUS Understanding Its Concepts and Methods

Sine function

The trigonometric functions are circular functions, because they are defined in terms of a circle.

Draw a circle of radius 1 with center at the origin.

Draw a line from the origin at an angle *q* to the positive *x*-axis.

The line intersects the circle at a point
(*x*,*y*) as shown
in the following figure:

The sine
of the angle *q* is defined
to be sin *q* = *y*.
In the figure, the arc length on the circle is equal to the
horizontal red (if negative) or green (if positive) line segment.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.