Question

use the (x,y) coordinates in the figure to find the value of the trigonometric function at the indicated real number, t, or state that the expression is undefined. \\(\sin \frac{\pi}{2}\\) select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\(\bigcirc\\) a. \\(\sin \frac{\pi}{2} = \square\\) (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) \\(\bigcirc\\) b. the expression is undefined.

Explanation:

Step1: Identify coordinate for $t=\frac{\pi}{2}$

From the unit circle, the coordinate at $t=\frac{\pi}{2}$ is $(0,1)$.

Step2: Recall sine definition on unit circle

For a unit circle coordinate $(x,y)$, $\sin t = y$.

Answer:

A. $\sin \frac{\pi}{2} = 1$