Question

Use the even–odd properties to find the exact value of each expression. Do not use a calculator.

$\csc (-{30}^{\mathrm{o}})$

Short answer

The exact value of trigonometric function is -2.

Step-by-step solution

Step 1. Given Information

Given that the trigonometric function is $\csc (-{30}^{\mathrm{o}}).$To find the exact value of trigonometric function using even odd property.

Step 2. Even odd property

On using even odd property,

$$\begin{gathered} \csc (-\mathrm{\theta })=\frac{1}{\sin (-\mathrm{\theta })} \\ =\frac{1}{-\mathrm{sin\theta }} \\ =\frac{1}{-\mathrm{y}} \end{gathered}$$

On substituting the value,

$$\begin{gathered} \csc (-{30}^{\mathrm{o}})=\frac{1}{\sin (-{30}^{\mathrm{o}})} \\ =\frac{1}{-\sin {30}^{\mathrm{o}}} \\ =\frac{1}{-{\displaystyle \frac{1}{2}}} \\ \csc (-{30}^{\mathrm{o}})=-2 \end{gathered}$$