# Question on trigonometric equations?

• Jun 26th 2008, 04:33 AM
fardeen_gen
Question 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.

• Jun 26th 2008, 04:50 AM
Moo
Hello,

Quote:

Originally Posted by fardeen_gen
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.

$\displaystyle \cos 2t=2 \cos^2t-1$

--> $\displaystyle \cos \theta=2 \cos^2 \frac{\theta}{2}-1$

-----> $\displaystyle 2 \cos^2 \frac{\theta}{2}=1+\cos \theta$

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 AM
fardeen_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)