Question

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

Answer 1

`2kpi` such that `k` is represents all integers

Explanation:

We revert the inverse function as follows:

`sec^-1(1)=x`
`sec(x)=1`
`1/cosx=1`
`cosx=1`
Thus `x` must be an integral multiple of `2pi`. This is because whenever x is an integral multiple of `2pi`, `cosx=1`.