Question

What is the exact value of `sec^-1 (sqrt2)`?

Answer 1

`sec^(-1)(sqrt(2)) = pi/4` or `(5pi)/4` (radians)
`color(white)("XXXX")`if restricted to `[0,2pi)`

Explanation:

If `sec^(-1)(sqrt(2)) = theta`
then
`color(white)("XXXX")` `sec(theta) = sqrt(2)`
`color(white)("XXXX")` `color(white)("XXXX")`by definition of inverse trig function

`rArr cos(theta) = 1/sqrt(2)`

This is a standard trigonometric triangle as pictured below.
`color(white)("XXXX")`(`45^o = pi/4` radians)