Find the exact value of the real number y.
-$$y = \csc ^ { - 1 } ( - 1 )$$
A) $2 \pi$
B) $\frac { \pi } { 4 }$
C) $\pi$
D) $- \frac { \pi } { 2 }$

Question

Quizplus · Accepted Answer

The cosecant function, $\csc(x)$, is the reciprocal of the sine function, $\sin(x)$. Therefore, $\csc(x) = \frac{1}{\sin(x)}$. The value of $\csc^{-1}(-1)$ corresponds to the angle whose cosecant is -1. Since $\csc(x) = \frac{1}{\sin(x)}$, we are looking for an angle whose sine is -1. The sine of $-\frac{\pi}{2}$ is -1, making it the correct answer.

Find the Exact Value of the Real Number Y y=csc⁡−1(−1)y = \csc ^ { - 1 } ( - 1 )y=csc−1(−1)

Find the Exact Value of the Real Number Y $y = \csc ^ { - 1 } ( - 1 )$