Thread: Need help solving this equation −sin (2θ) − cos (4θ) = 0

1. Need help solving this equation −sin (2θ) − cos (4θ) = 0

Can someone help explain to me how to use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). I have tried for some time and have been having quite of bit of difficulty on figuring out how to proceed. Any input will be sincerely appreciated.

2. Re: Need help solving this equation −sin (2θ) − cos (4θ) = 0

To make things simpler perhaps, I would suggest letting $u=2\theta$ where $0\le u<4\pi$ and so the equation becomes:

$-\sin(u)-\cos(2u)=0$

I would suggest using the double-angle identity for cosine $\cos(2\theta)=1-2\sin^2(\theta)$ this was you will obtain a quadratic in $\sin(u)$ which factors nicely.

Can you proceed?