Cos -1 (- sqrt 2/2)

Question

same as the question above

Answer 1

You're looking for arccos (-√2/2) a.k.a. arccos (1/√2).

The presence of this square root of 2, over 2 should bring to mind a Reference Triangle of the type 45-45-90.

Negative cosines occur in Quadrant II.  Therefore the answer is 135^o, also known as 3pi/4.

 

Answer 2

The range for f(x) = Cos^-1 x  is [0, π].

If cos x = -√2/2, then x is in the second Quadrant.

 

x = 3π/4