Question

final exam (precalculus) score: 21/25 answered: 21/25 question 22 evaluate the following expressions. your answer must be an angle in radians and in the interval -π/2, π/2. (a) sin⁻¹(1)= (b) sin⁻¹(-1)= (c) sin⁻¹(1/2)=

Explanation:

Step1: Recall inverse - sine values

The inverse - sine function, $\sin^{-1}(x)$, gives an angle $\theta$ such that $\sin(\theta)=x$ and $\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]$.

Step2: Solve (a)

We know that $\sin(\frac{\pi}{2}) = 1$, so $\sin^{-1}(1)=\frac{\pi}{2}$.

Step3: Solve (b)

Since $\sin(-\frac{\pi}{2})=-1$, then $\sin^{-1}(-1)=-\frac{\pi}{2}$.

Step4: Solve (c)

As $\sin(\frac{\pi}{6})=\frac{1}{2}$, so $\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$.

Answer:

(a) $\frac{\pi}{2}$
(b) $-\frac{\pi}{2}$
(c) $\frac{\pi}{6}$