Chapter 4.7, Problem 19E

Solution

To find: find the approximate value and express your results in radians.

Approximate value of ${\sin }^{-1}\left(-0.46\right)$ is $-\text{0}\text{.48 radians}$ .

Given: ${\sin }^{-1}\left(-0.46\right)$

Concept Used: inverse trigonometric $\theta ={\sin }^{-1}x,\theta \in \left[-\frac{\pi }{2},\frac{\pi }{2}\right]$

Calculation:

  ${\sin }^{-1}\left(-0.46\right)$

value of ${\sin }^{-1}\left(-0.46\right)$ is $-0.477995199\approx -0.48\text{ radians}$

Conclusion:

Approximate value of ${\sin }^{-1}\left(-0.46\right)$ is $-\text{0}\text{.48 radians}$ .