# Homework Help: Intersections of two graphs (polar coordinates)

1. Jan 13, 2007

### kasse

1. The problem statement, all variables and given/known data

Find all points of intersection of the two graphs r=sin $$\theta$$ and r=cos 2 $$\theta$$

3. The attempt at a solution

sin $$\theta$$ = cos 2 $$\theta$$

I use the trigonometric identity cos 2x = (cosx)^2 - (sinx)^2 but it doesn't take me any further.

Last edited by a moderator: Jan 13, 2007
2. Jan 13, 2007

### Hootenanny

Staff Emeritus
Don't forget cos2x = 1 - sin2x

You should be able to form a quadratic expression in sin(x), which you can solve using the quadratic formula.

3. Jan 13, 2007

### turdferguson

Thats how you derive the alternate double angle identities, which are meant for a problem like this because they put cos2x in terms of one function