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.)