Answer:
Explanation:
3√2 sec(x) + 2 = 2√2 sec(x) Subtract 2√2 sec(x) from both sides
√2 sec(x) + 2 = 0 Subtract 2 from both sides.
√2 sec(x) = - 2
The secant is related to the cosine. sec(x) = 1/cos(x). The statement tells you that wherever the cos(x) < 0 , the secant will be as will. That means your answer will be in quad 2 and quad 3 and you are to use the appropriate rules for theta in those two quads.
It turns out that you could do this by using the reciprocal of 2
cos-1(- 0.5) = 120 degres. In terms of pi (which is 180 degrees)
120/180 * pi = (2/3) * pi
In quad three you would get pi + pi/3 = 4/3 pi
So your answers are
2/3 pi and 4/3 pi