Chapter 6 - 6.3 - Trigonometric Functions of Any Angle - 6.3 Exercises - Page 454: 65

$csc\theta = \sqrt 10$

Note: $sin\theta = \frac{opp}{hyp}$ $cos\theta = \frac{adj}{hyp}$ $tan\theta = \frac{opp}{adj}$ $cot\theta = -3$ The equivalent is: $tan\theta = \frac{-1}{3}$ We must find the Hypotenuse: $\sqrt {1^{2}+3^{2}} = \sqrt 10$ We can then solve for $csc\theta$: $sin\theta = \frac{1}{\sqrt 10}$ Therefore, $csc\theta = \sqrt 10$