Find all the angles θ between -π to π that satisfy the equation 5 cos 2θ + 2 cos^2 θ/2 + 1 = 0?
The given answer includes + or - π/6, π - cos^-1 3/5 and -π + cos ^-1 3/5.
My own answers are not matching. Please help!
Find all the angles θ between -π to π that satisfy the equation 5 cos 2θ + 2 cos^2 θ/2 + 1 = 0?
The given answer includes + or - π/6, π - cos^-1 3/5 and -π + cos ^-1 3/5.
My own answers are not matching. Please help!
Hello,
$\displaystyle \cos 2t=2 \cos^2t-1$
--> $\displaystyle \cos \theta=2 \cos^2 \frac{\theta}{2}-1$
-----> $\displaystyle 2 \cos^2 \frac{\theta}{2}=1+\cos \theta$
Going back to the equation :
$\displaystyle 5 \cos 2 \theta+(1+\cos \theta)+1=0$
But $\displaystyle \cos 2 \theta=2\cos^2 \theta-1$
---> $\displaystyle 5 (2\cos^2 \theta-1)+\cos \theta+2=0$
$\displaystyle 10 \cos^2 \theta-5+\cos \theta+2=0$
$\displaystyle \boxed{10 \cos^2 \theta+\cos \theta-3=0}$
Substitute $\displaystyle y=\cos \theta$ and you're done
If you still can't get to the solution, show your working