We want to find the value of cos⁻¹ x, where [tex]x = - \frac{ \sqrt{2} }{2} [/tex]
Note that
cos(45°) = sin(45°) = 1/√2; tan(45°) = 1.
Also,
45° = π/4 radians, and
√2/2 = 1/√2
The cosine function is negative in quadrants 2 and 3.
Therefore
cos⁻¹ (-√2/2) = π - π/4 radians = (3/4)π radians or
= π + π/4 radins = (5/4) radians
In degrees,
cos (-√2/2) = 135° or 225°
Answer:
[tex] \frac{3 \pi }{4}\,or\, \frac{5 \pi }{4}\,radians [/tex]
In degrees, it is 135° or 225°.
