Write the expression and evaluate. There is only one answer whIch should match the range of the inverse trig function.

Question

Sec^-1(-2)
Sec^-1(-sqrt2)
Tan^-1(-sqrt3)
Tan^-1(sqrt3)

Answer 1

I will do the 2nd one:

sec^-1 (-√2) = Ø , such that sec Ø = -√2
or
cos Ø = -1/√2
I know that cos 45° = 1/√2
but the cosine is negative in II and III
so Ø = 180-45° = 135°
or Ø = 180+45 = 225°

They probably expect the answer of 135° or 3π/4 radians

Answer 2

How did you come up with 135 being the answer? I understand what you did but you said it could also be 225, so what makes you pick 135?

Answer 3

Also doesnt the cos45 = sqrt2/2 not 1/sqrt 2?

Answer 4

yes, because sqrt2/2 = 1/sqrt2