Question

How do you find ALL solutions of the equation below in the interval [0, 2π) for `9sec^2(x)-12=0`?

Answer 1

`f(x) = 9.(1/cos^2 x) - 12 = 0,` Let cos = t

`f(t) = 12t^2 - 9 = 3(4t^2 - 3) = 0`

`4t^2 = 3 -> t = (sqr3)/2, and t = -(sqr3)/2`

a. `t = cos x = (sqr3)/2` -> x = 30 deg

b `x = -(sqr3)/2`= 150 deg

Within interval (0, 2pi), there are 2answers: 30 and 150