Question

use the unit - circle, along with the definitions of the circular functions, to find the exact values for the given functions when s = -\\(\frac{\pi}{2}\\). select the correct choice below and fill in any answer boxes in your choice.
a. \\(\sin(-\frac{\pi}{2})=\\) (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
b. the solution is undefined.

Explanation:

Step1: Recall sine - function property

The sine function \(y = \sin(x)\) has the property \(\sin(-x)=-\sin(x)\). Here \(x = \frac{\pi}{2}\), so \(\sin(-\frac{\pi}{2})=-\sin(\frac{\pi}{2})\).

Step2: Evaluate \(\sin(\frac{\pi}{2})\)

We know from the unit - circle definition that \(\sin(\frac{\pi}{2}) = 1\). Then \(-\sin(\frac{\pi}{2})=-1\).

Answer:

A. - 1