# Solving a trigonometric equation.

• Apr 26th 2010, 07:08 AM
JennyFlowers
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? :)
• Apr 26th 2010, 07:14 AM
Gusbob
Quote:

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.