Question

which is equivalent to $sin^{-1}(0.75)$? round your answer to the nearest hundredth of a radian.
-1.33
-0.75
0.68
0.85

Explanation:

Step1: Recall the inverse sine function

The inverse sine function, \( \sin^{-1}(x) \), gives the angle \( \theta \) (in radians or degrees) such that \( \sin(\theta)=x \), where \( -1\leq x\leq 1 \) and \( -\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2} \) (for radians). Here we need to find \( \sin^{-1}(0.75) \) in radians.

Step2: Use a calculator to compute \( \sin^{-1}(0.75) \)

We use a calculator in radian mode. When we calculate \( \sin^{-1}(0.75) \), we get approximately \( 0.848062\cdots \)

Step3: Round to the nearest hundredth

Rounding \( 0.848062\cdots \) to the nearest hundredth (two decimal places), we look at the third decimal place which is 8. Since \( 8\geq5 \), we round up the second decimal place. So \( 0.848062\cdots\approx 0.85 \)

Answer:

D. 0.85