# Thread: Solve for the indicated variable:

1. ## Solve for the indicated variable:

cos^2x+3cos^2x+2=0 How do you solve this?

2. ## Re: Solve for the indicated variable:

If you wright:
$\cos^2(x)+3\cos^2(x)+2=0 \Leftrightarrow 4\cos^2(x)=-2 \Leftrightarrow \cos^2(x)=\frac{-1}{2}$

What do you notice?

3. ## Re: Solve for the indicated variable:

Originally Posted by CprlCaboose
cos^2x+3cos^2x+2=0 How do you solve this?
There might be a typo... (and yes, I have sobered-up since this morning!)

$cos^2(x) + 3cos(x) + 2 = 0$ implies

$(cosx + 2)(cosx + 1) = 0$
...
Only in case of typo!

4. ## Re: Solve for the indicated variable:

cos^2 x + 3 cos^2 x+2=0

4 cos^2 x = -2

cos^2 x = -1/2

cos x = plus or minus -1/2

x lies in the 1st, 2nd, 3rd and 4th quadrant since it has positive and negative values. Now find the basic angle $\alpha$ and solve for the 4 possible angles.

5. ## Re: Solve for the indicated variable:

Originally Posted by PythagorasNeophyte
cos^2 x = -1/2

cos x = plus or minus -1/2
That's not true, if the equation was:
$\cos^2(x)=\frac{1}{4}$
Then you were right, because then:
$\cos(x)=\pm \frac{1}{2}$

Also, look at the graph of the function $4\cos^2(x)+2$:
http://www.wolframalpha.com/input/?i=4cos^2%28x%29%2B2

What do you notice?