Question 191792
If you look at the unit circle:


<img src="http://www.math.ucsd.edu/%7Ejarmel/math4c/Unit_Circle_Angles.png">




You'll see that at the point on the circle that has the x-coordinate {{{x=sqrt(2)/2}}} (in the first quadrant), the angle is {{{pi/4}}} or 45 degrees.



So this means that *[Tex \LARGE \cos^{-1}\left(\frac{\sqrt{2}}{2}\right)=\frac{\pi}{4}] (in radians) or *[Tex \LARGE \cos^{-1}\left(\frac{\sqrt{2}}{2}\right)=45] (in degrees)