Find the exact value in degrees. Sin^-1(square root 2/2)

Answer 1

To find the exact value in degrees of arcsine of square root 2/2, we can start by using the definition of arcsine:

sin^(-1)(square root 2/2) = θ

This equation implies that the sine of θ is equal to √2/2:

sin(θ) = √2/2

We know that for an angle θ, if its sine is √2/2, then it must be one of the special angles on the unit circle where the coordinates of a point on the circle are (√2/2, 1/2) — these angles are 45 degrees and 135 degrees in the first and second quadrants, respectively.

So we have two possible values for θ, which are 45 degrees and 135 degrees.