Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.2 - Trigonometric Functions: The Unit Circle - Exercise Set - Page 549: 97

Answer

The statement makes sense.

Work Step by Step

The coordinates of point A, if point A makes an angle $\theta $ with the positive x-axis, will be $\left( x,y \right)\equiv \left[ OA\cos \theta ,OA\sin \theta \right]$ where O is the origin and OA is the radius of the unit circle. Since it is a unit circle, the length of OA is equal to 1 unit. Therefore, $\begin{align} & \left( x,y \right)\equiv \left[ 1\times \cos \theta ,1\times \sin \theta \right] \\ & \equiv \left[ \cos \theta ,\sin \theta \right] \end{align}$ Thus, its coordinates define the cosine and sine functions, respectively. Thus, the statement is true.
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