Find two exact values of theta in degrees (0 less than or equal to theta < 360°) if cos theta = -(square root of 2)/2.

Answer 1

cosØ = -√2/2
so Ø is in quadrants II or III

you should know the trig ratios of the 45-45-90 as well as the 30-60-90 degree triangles.
so you know the angle in standard position is 45°, because cos45 = √2/2

so Ø = 180-45 or 135° (in II)
or Ø = 180+45 = 225° (in III)