# Chapter 3 - Section 3.3 - Definition III: Circular Functions - 3.3 Problem Set - Page 143: 17

$\csc\frac{7\pi}{4}$ = -$\sqrt 2$

#### Work Step by Step

Recall: $\csc\theta$ = $\frac{1}{\sin\theta}$ Recall Definition 3: $\sin\theta$ = y Substitute: $\csc\frac{7\pi}{4}$ = $\frac{1}{\sin\frac{7\pi}{4}}$ $\csc\frac{7\pi}{4}$ = $\frac{1}{\frac{-\sqrt 2}{2}}$ $\csc\frac{7\pi}{4}$ = $\frac{1}{1} \times \frac{2}{-\sqrt 2}$ $\csc\frac{7\pi}{4}$ = $\frac{2}{-\sqrt 2} \times (\frac{\sqrt 2}{\sqrt 2})$ $\csc\frac{7\pi}{4}$ = $\frac{2\sqrt 2}{-2}$ $\csc\frac{7\pi}{4}$ = $-\sqrt 2$

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