# trig problems

• Apr 19th 2009, 06:46 PM
deltemis
trig problems
Hi guys, I'm having a little trouble with 2 problems.

The first is:

find all solutions to 2cos^2 theta + cos theta - 1 = 0, 0 <= theta <= 2pi, giving exact solutions

and the second is:

find all solutions to cos(2theta) + 5cos theta + 3 = 0, 0 <= theta <= 2pi, giving exact solutions

My problem is that I'm not sure as to how to approach and begin these problems. They look like I'm supposed to be using trig identities but when I tried that I simply confused myself.

Any help would be very much appreciated. Thanks in advanced.
• Apr 19th 2009, 07:05 PM
TheEmptySet
Quote:

Originally Posted by deltemis
Hi guys, I'm having a little trouble with 2 problems.

The first is:

find all solutions to 2cos^2 theta + cos theta - 1 = 0, 0 <= theta <= 2pi, giving exact solutions

and the second is:

find all solutions to cos(2theta) + 5cos theta + 3 = 0, 0 <= theta <= 2pi, giving exact solutions

My problem is that I'm not sure as to how to approach and begin these problems. They look like I'm supposed to be using trig identities but when I tried that I simply confused myself.

Any help would be very much appreciated. Thanks in advanced.

The first one can be factored compare to this equation with

$\displaystyle x=\cos(\theta)$

$\displaystyle 2x^2+x-1=0 \iff (2x-1)(x+1)=0$

for the second use the identity

$\displaystyle \cos(2\theta)=2\cos^{2}(\theta)-1$

Sub this in and then factor.