Question

(a) Solve for all values of cos x to the nearest tenth.
4 cos2 x = cos x + 2
(b) How many values of x between 180 degrees and 360 degrees satisfy the equation 4 cos2 x = cos x + 2?

Answer 1

maybe this identity could be useful
cos(2x)=cos^2(x)-sin^2(x)
=cos^2(x)-(1-cos^2(x))
=2cos^2(x)-1

Answer 2

But how am I suppose to use this identity to find the values of x ??

Answer 3

you will have a quadtratic equation in terms of cos

Answer 4

\[4 \cos(2x)=\cos(x)+2 \\ 4(2 \cos^2(x)-1)=\cos(x)+2 \\8\cos^2(x)-4=\cos(x)+2 \\ 8\cos^2(x)-\cos(x)-6=0\]
use the quadratic formula to solve for cos(x)

Answer 5

then you can solve for x