## moongazer 5 years ago 4 cos2 ϴ = 3 find ϴ?

1. moongazer

or is it a typo?

2. anonymous

$4cos(2ϴ)=3$$cos(2ϴ)=\frac{3}{4}$$2ϴ=2n\pi+cos^{-1}(\frac{3}{4})$$ϴ=n\pi+\frac{1}{2}cos^{-1}(\frac{3}{4})$ where n is an integer

3. dumbcow

OR cos(2x) = 3/4 cos^2 - sin^2 = 3/4 cos^2 -(1-cos^2) = 3/4 2cos^2 -1 = 3/4 2cos^2 = 7/4 cos^2 = 7/8 cos(x) = +-sqrt(7)/2sqrt2

4. dumbcow

its more likely cos^2 rather than cos(2x) in this case ->cos^2 = 3/4 cos(x) = +-sqrt3/2 x = pi/6, 5pi/6

5. anonymous

i think you're right @dumbcow i didn't even think about the cos^2 :)