Question

use the even - odd properties of the trigonometric functions to find the exact va
\\( \sin ( - 45 ^ { \circ } ) \\)
select the correct choice below and fill in any answer boxes in your choice.
\\( \bigcirc \\) a. \\( \sin ( - 45 ^ { \circ } ) = \\)
(simplify your answer, including any radicals. use integers or fractions
\\( \bigcirc \\) b. the answer is undefined.

Explanation:

Step1: Recall the odd - function property of sine

The sine function has the property \( \sin(-\theta)=-\sin\theta\).

Step2: Substitute \(\theta = 45^{\circ}\)

We know that \( \sin(45^{\circ})=\frac{\sqrt{2}}{2}\).
Using the odd - function property \( \sin(-45^{\circ})=-\sin(45^{\circ})\).
Substituting the value of \( \sin(45^{\circ})\), we get \( \sin(-45^{\circ})=-\frac{\sqrt{2}}{2}\).

Answer:

A. \( \sin(-45^{\circ})=-\frac{\sqrt{2}}{2}\)