Answer:
[tex]\frac{3\pi}{4}[/tex]
(Assuming you want your answer in radians)
If you want the answer in degrees just multiply your answer in radians by [tex]\frac{180^\circ}{\pi}[/tex] giving you:
[tex]\frac{3\pi}{4} \cdot \frac{180^\circ}{\pi}=\frac{3(180)}{4}=135^{\circ}[/tex].
We can do this since [tex]\pi \text{ rad }=180^\circ[/tex] (half the circumference of the unit circle is equivalent to 180 degree rotation).
Step-by-step explanation:
[tex]\cos^{-1}(x)[/tex] is going to output an angle measurement in [tex][0,\pi][/tex].
So we are looking to solve the following equation in that interval:
[tex]\cos(x)=-\frac{\sqrt{2}}{2}[/tex].
This happens in the second quadrant on the given interval.
The solution to the equation is [tex]\frac{3\pi}{4}[/tex].
So we are saying that [tex]\cos(\frac{3\pi}{4})=\frac{-\sqrt{2}}{2}[/tex] implies [tex]\cos^{-1}(\frac{-\sqrt{2}}{2})=\frac{3\pi}{4}[/tex] since [tex]\frac{3\pi}{4} \in [0,\pi][/tex].
Answer is [tex]\frac{3\pi}{4}[/tex].
