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

1 Answer
Oct 13, 2015

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.)