Answer:
-π/4
Step-by-step explanation:
You want the angle in radians whose sine is -(√2)/2.
Sine
You recall from memory that sin(45°) = (√2)/2, and you know the sine is negative for negative angles in the range -180° to 0°. The inverse sine function has a range of -90° to +90°, so ...
[tex]\sin^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)=-45^\circ=\boxed{-\dfrac{\pi}{4}\text{ radians}}[/tex]
