Chapter 1.6, Problem 28E

To determine

To find: The measure of angle ${\sin }^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ in radian and degree.

Answer to Problem 28E

Themeasure of angle in radian is $-0.785$ and degrees is $-45°$ .

Explanation of Solution

Given information:The given angleis ${\sin }^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ .

Calculation:

To find the conversion of given angle into radian, use the calculator and enter the keystrokes.

  $\boxed{2\text{nd}}\boxed{\text{SIN}}\boxed{(-)}\boxed{2\text{nd}}\boxed{x^2}\boxed{2}\boxed{)}\boxed{÷}\boxed{2}\boxed{)}$

Press $\boxed{\text{MODE}}$ and select the radian mode then quit the window. Now, press $\boxed{\text{ENTER}}$ key.

  ${\sin }^{-1}\left(-\frac{\sqrt{2}}{2}\right)=-0.785$

To find the conversion of given angle into degree, use the calculator and enter the keystrokes.

  $\boxed{2\text{nd}}\boxed{\text{SIN}}\boxed{(-)}\boxed{2\text{nd}}\boxed{x^2}\boxed{2}\boxed{)}\boxed{÷}\boxed{2}\boxed{)}$

Select the degree mode then quit the window. Now, press $\boxed{\text{ENTER}}$ key.

  ${\sin }^{-1}\left(-\frac{\sqrt{2}}{2}\right)=-45°$

Therefore, the measure of angle in radian is $-0.785$ and degrees is $-45°$ .