Question

How do you find two solutions (in degree and radians) for `secx = sqrt2`?

Answer 1

The two solutions in degrees (from 0 to 360) would be 45 and 315.
In radians (from 0 to `2pi`) the answer would be `pi/4` and `(7pi)/4`

Explanation:

`sec(x) = 1/cos(x)`

Plug in our givens:

`sqrt(2) = 1/cos(x)`
`cos(x) = 1/sqrt(2)`
`cos(x) = sqrt(2)/2`

Using the unit circle, I know that `cos(45)` or `cos(pi/4)` are equal to `sqrt(2)/2`, and therefore I can determine that 45 or `pi/4` are one of the angles.

We also know that the value at `-pi/4` or `-45` are equal to `sqrt(2)/2`, and so we can have this as our second angle (`-pi/4` can be written as a negative, or as `(7pi)/4` and same goes for -45, which would instead be 315.)