Question

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

$\sin (-{135}^{\mathrm{o}})$

Short answer

The exact value of trigonometric expression is$-\frac{\sqrt{2}}{2}.$

Step-by-step solution

Step 1. Given Information

Given that the trigonometric function is $\sin (-{135}^{\mathrm{o}}).$To find the exact value of trigonometric function using even odd property.

Step 2. Even odd property

On using the even odd property,

$$\begin{gathered} \sin (-\mathrm{\theta })=-\mathrm{sin\theta } \\ \sin (-{135}^{\mathrm{o}})=-\sin {135}^{\mathrm{o}} \\ =-\frac{1}{\sqrt{2}} \\ \sin (-{135}^{\mathrm{o}})=-\frac{\sqrt{2}}{2} \end{gathered}$$