Question

How do you evaluate `sec^-1(-2)`?

Answer 1

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

Explanation:

From definition of inverse ratio if `secx=-2`, `sec^(-1)(-2)=x` and range is `[0,pi}`

We know that secant function is negative in `Q2`

as `sec(pi/3)=2`, we have `sec(pi-pi/3)=sec((2pi)/3)=-2`

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