Inverse trig function question

Question

How would I find the inverse trig function of the below equation?

Q: arcsec(-(2sqrt3)/(3))

Answer 1

Answer 2

x=arcsec(-2sqrt(3)/3)

sec x = -2sqrt(3)/3

cos x = -sqrt(3)/2

If the cos were positive, your answer would be 30°.

Since it is negative, x=150°.

How do I know this? In a 30-60 right triangle, the sides are in this proportion 2:1:√3.