Intersections of two graphs (polar coordinates)

[kasse]

Homework Statement

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

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.

 

[Hootenanny]

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.

 

[turdferguson]

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.

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