Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises - Page 37: 63

$\csc\theta=\frac{\sqrt 5}{-2}$

1. We get the values from the cotangent: $x=1$ $y=-2$ 2. Since x is positive and y is negative, the angle is in the IV quadrant. 3. We can calculate r using x and y by applying distance formula $r=\sqrt {(1)^{2}+(-2)^{2}}=\sqrt 5$ 4. Then just insert those values: $\csc\theta=\frac{\sqrt 5}{-2}