Solution:
sec x = -4 , sec x = 1/ cos x , and cos x = 1/sec x = -1/4 = -0.25 take cos-1 for both sides
cos-1cosx = cos-1 ( -0.25) . x = 104.5° , converting to radians x = 104.5° ( π/ / 180°) = 1.82 rad
the set of solutions for x = x + 2πn where n is the number of 2π revolutions or full circle and back to the original point n = { 1, ∞} , For illustration only we will only take n = 1, 2, 3 and solve
x = 1.82 rad + 2π(1) rad = 1.82 rad + 6.28 rad = 8.1 rad
x = 1.82 rad + 2π(2) rad = 1.82 rad + 12.56 rad = 14.38 rad
x = 1.82 rad + 2π(3) rad = 1.82 rad + 18.84 rad = 20.67 rad and so on
Spot check last answer cos ( 20.67 rad) = -0.247 approximately -0.25 or -1/4 and it checks. you can do checks for the other values if you wish but remember to set your calculator to radians
