Question

Solve "6 cos (2x) - 2 sin (x) = 4" for [0,2Pi)

Answer 1

double angle identity:

cos(2x) = 1-2sin^2

Answer 2

treat it like a quadratic equation, set equal to 0

--> 12sin^2 +2sin -2 = 0

Answer 3

I never thought of that! Hold on

Answer 4

sin x = y
12y^2 + 2y - 2 = 0
(4y + 2)(3y - 1) = 0
y = -1/2 or y = 1/3

Answer 5

very good, not use inverse sine to get x values

Answer 6

now*

Answer 7

sin x = -1/2
x = -.523598

sin x = 1/3
x = .339836

Answer 8

Would I have to turn this into a "better looking" value? Such as pi over a number?

Answer 9

yes but remember x is in [0,2pi] make it positive angle
also use unit circle, there should be 4 total solutions

Answer 10

Right, how would you go about doing that?

Answer 11

for sin x = -1/2, yes its x = -pi/3
but for the other one there is no "nice" value

Answer 12

find the angles