Question

How do you evaluate `sec^-1(2/sqrt3)` without a calculator?

Answer 1

`sec^(-1)(2/sqrt(3)) = pi/6`

Explanation:

Find `x` such that `sec x = 2/sqrt(3)`

As:

`secx = 1/cosx`

this is the same as finding `x` such that `cos x =sqrt(3)/2` and we know that:

`cos(pi/6) = sqrt(3)/2`