# Homework Help: Solving trigonometric equations

1. Oct 9, 2011

### davidp92

1. The problem statement, all variables and given/known data
How do you solve cosx=-cos2x?

3. The attempt at a solution
I've tried graphing it, but just wasn't able to crack the solutions

Thanks for help!

2. Oct 9, 2011

### ehild

What is the relation between two angles a and b if cos(a)=-cos(b)? Look at the unit circle.

Or use the formula cos(2x)=cos^(x)-sin^2(x)

hild

3. Oct 9, 2011

### tensorit

If you merely want the answer (without proof), type "solve cos(x)=-cos(2x) for x" in wolfram alpha. If you want to figure out the proof, look up the trig formula that lets you express cos(2x) in terms of cos(x). With that substitution, you will have transformed your equation into a quadratic equation, with cos(x) as the unknown, the solution of which is cos(x)=-1 (implying x=-pi) or cos(x)=1/2 (implying x=pi/3 or x=-pi/3). Of course, add any integer multiple of 2pi to these answers to characterize the infinite number of solutions.

4. Oct 9, 2011

### SammyS

Staff Emeritus
or use cos(2x) = 2cos2(x) - 1