Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises - Page 58: 8

Answer

Using the reference angle $\theta'$, we can find the values of the trigonometric functions as follows: $sin~\theta = -sin~\theta'$ $cos~\theta = -cos~\theta'$ $tan~\theta = tan~\theta'$ $csc~\theta = -csc~\theta'$ $sec~\theta = -sec~\theta'$ $cot~\theta = cot~\theta'$

Work Step by Step

Let $\theta$ be an angle in quadrant III. We can find a reference angle $\theta'$ in quadrant I. $\theta' = \theta - 180^{\circ}$ In quadrant I, all the trigonometric functions have positive values. However, in quadrant III, only $tan~\theta$ and $cot~\theta$ have positive values, while $sin~\theta$, $cos~\theta$, $csc~\theta$, and $sec~\theta$ have negative values. Using the reference angle $\theta'$, we can find the values of the trigonometric functions as follows: $sin~\theta = -sin~\theta'$ $cos~\theta = -cos~\theta'$ $tan~\theta = tan~\theta'$ $csc~\theta = -csc~\theta'$ $sec~\theta = -sec~\theta'$ $cot~\theta = cot~\theta'$
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