Find sin(t) given t= 5pie/2

What is the value of $\sin\left(\frac{5\pi}{2}\right)$?

Well, first, let's determine the quadrant or quadrantal where the terminal side lies. Rotating counterclockwise by $\frac{5\pi}{2}$ radians exceeds one revolution, and the terminal side will land on the first quadrantal:

$\sin(\frac{5\pi}{2})=\sin(\frac{\pi}{2})=1$