# Thread: Solving a trigonometric equation.

1. ## Solving a trigonometric equation.

Hey guys!

I need help solving the following trigonometric equation:

$\displaystyle 7 cos x = 4 - 2 sin^2 x$

I get:

$\displaystyle 7 cos x = 4 -2(1-cos^2 x)$
$\displaystyle 7 cos x = 4 -2 + 2 cos^2 x$
$\displaystyle 2 cos^2 x - 7 cos x + 2 = 0$

It turns out this doesn't factor very well, and I'm almost sure I made a mistake. None of the problems I'm working on require the quadratic equation so I'm pretty sure that I just solved the equation incorrectly.

Help? 2. Originally Posted by JennyFlowers Hey guys!

I need help solving the following trigonometric equation:

$\displaystyle 7 cos x = 4 - 2 sin^2 x$

I get:

$\displaystyle 7 cos x = 4 -2(1-cos^2 x)$
$\displaystyle 7 cos x = 4 -2 + 2 cos^2 x$
$\displaystyle 2 cos^2 x - 7 cos x + 2 = 0$

It turns out this doesn't factor very well, and I'm almost sure I made a mistake. None of the problems I'm working on require the quadratic equation so I'm pretty sure that I just solved the equation incorrectly.

Help? Hey,

Unfortunately, you do need to use the quadratic equation this time (there is a way to complete the square but that's a mess as well).

Good luck with that. I've seen the answer and it isn't pretty, so don't get discouraged if things become messy.

#### Search Tags

equation, solving, trigonometric 