Question

find the exact value of the real number y in the equation Y=arcsin(-√3/2)

Answer 1

it's pi/3

Answer 2

Find -sqrt3/2 on unit circle for sin.....what is the corresponding angle?

Answer 3

\[Y=-\dfrac{\pi}{3}\]because\[\sin(Y)=\sin\left(-\dfrac{\pi}{3}\right)=-\dfrac{\sqrt 3}{2}\] and \[-\dfrac{\pi}{2}\le Y \le \dfrac{\pi}{2},\] which is the domain of the arcsine function.