How do I solve sec(2x)-7=0 for the four smallest positive solutions?

More specifically, I have no clue how to get rid of the sec of the equation.

1 Answer
Jun 27, 2018

40^@89; 139^@11

Explanation:

sec 2x = 7
cos 2x = 1/(sec 2x) = 1/7
Calculator and unit circle give 2 solutions for 2x:
2x = +- 81^@78 + k360^@
a. 2x = 81^@78 + k360^@
x = 40^@89 + k180
If k = 0 --> x = 40^@89,
If k = 1 --> x = 40.89 + 180 = 220^@89
b.. 2x = - 81^@78 + k360^@, or
2x = 278^@22 + k360^@ (co-terminal)
x = 139^@11 + k180^@
The 2 smallest positive answers are:
40^@89; 139^@11