Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.2 Trigonometric Functions: Unit Circle Approach - 5.2 Assess Your Understanding - Page 403: 51

Answer

1. $sin\frac{3\pi}{4}= \frac{\sqrt 2}{2}$. 2. $cos\frac{3\pi}{4}= -\frac{\sqrt 2}{2}$. 3. $tan\frac{3\pi}{4}= -1$. 4. $cot\frac{3\pi}{4}= -1$. 5. $sec\frac{3\pi}{4}= -\sqrt 2$. 6. $csc\frac{3\pi}{4}= \sqrt 2$.

Work Step by Step

1. $sin\frac{3\pi}{4}=sin(\pi-\frac{3\pi}{4})=sin\frac{3\pi}{4}=\frac{\sqrt 2}{2}$. 2. $cos\frac{3\pi}{4}=cos(\pi-\frac{3\pi}{4})=-cos\frac{3\pi}{4}=-\frac{\sqrt 2}{2}$. 3. $tan\frac{3\pi}{4}=tan(\pi-\frac{3\pi}{4})=-tan\frac{3\pi}{4}=-1$. 4. $cot\frac{3\pi}{4}=\frac{1}{tan\frac{3\pi}{4}}=-1$. 5. $sec\frac{3\pi}{4}=\frac{1}{cos\frac{3\pi}{4}}=-\sqrt 2$. 6. $csc\frac{3\pi}{4}=\frac{1}{sin\frac{3\pi}{4}}=\sqrt 2$.
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