Question

without using a calculator, evaluate or simplify the expression. csc⁻¹(1) select the correct answer below and, if necessary, fill in the answer box to complete your choice. a. csc⁻¹(1)= (type your answer in radians. use angle measures greater than or equal to -π/2 and less than or equal to π/2. type an exact answer, using π as needed.) b. there is no solution.

Explanation:

Step1: Recall csc definition

$\csc^{-1}(x)$ is inverse of $\csc(x)=\frac{1}{\sin(x)}$. We want $\csc^{-1}(1)$, so $\csc(y) = 1$, then $\sin(y)=1$.

Step2: Find y in given range

In the range $-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}$, when $\sin(y) = 1$, $y=\frac{\pi}{2}$.

Answer:

A. $\csc^{-1}(1)=\frac{\pi}{2}$