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!

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- Jun 26th 2008, 04:33 AMfardeen_genQuestion on trigonometric equations?
**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! - Jun 26th 2008, 04:50 AMMoo
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 - Jun 26th 2008, 05:10 AMfardeen_gen
Thanks moo. There is some problem with either my computer or the forum.I did not double post voluntarily. An extra post appeared earlier also with no fault of my own. Mods please take notice! (Worried)