# How do you express the value as a trigonometric function of an angle in Quadrant I given csc(-330^circ)?

Mar 11, 2018

color(blue)(csc (30) = 1 / sin 30 = (1 / (1/2)) = 2

#### Explanation:

$\theta = - {330}^{\circ}$ can be written as $- 330 + 360 = {30}^{\circ}$

${30}^{\circ}$ is an angle in the first quadrant where all the trigonometric functions are positive.

$\csc \left(30\right) = \frac{1}{\sin} 30 = \left(\frac{1}{\frac{1}{2}}\right) = 2$ from the table above, $\sin 30 = \frac{1}{2}$

$\csc \left(30\right) = \frac{1}{\sin} 30 = \left(\frac{1}{\frac{1}{2}}\right) = 2$