Approximate $\sin ^ { - 1 } ( - 0.51 )$. Round your answer to four decimal places.
A) $- 1.8685$
B) $- 2.0484$
C) $- 0.4882$
D) $- 0.5352$
E) $- 0.9249$

Question

Quizplus · Accepted Answer

We use the identity $\sin^{-1}(-x)=-\sin^{-1}(x)$ to get $\sin^{-1}(0.51)$. Since $0.5<0.51<0.6$, we expect $\sin^{-1}(0.51)$ to be slightly larger than $\sin^{-1}(0.5)=\frac{\pi}{6}=0.5236\dots$. Also, $\sin^{-1}(1)=\frac{\pi}{2}=1.5708\dots$ and $\sin^{-1}(0)=0$. Therefore, $\sin^{-1}(0.51)$ is slightly less than $\frac{\pi}{3}=1.0472\dots$, which means that $\sin^{-1}(-0.51)$ is slightly less than $-\frac{\pi}{3}=-1.0472\dots$. Rounded to four decimal places, this is equal to $\boxed{	extbf{(D)}\ -0.5352}$.

Approximate sin⁡−1(−0.51)\sin ^ { - 1 } ( - 0.51 )sin−1(−0.51)

Approximate $\sin ^ { - 1 } ( - 0.51 )$