## anonymous 5 years ago Convert r=1-Cos[2x] into rectangular. I tried using the trig identity of Cos2x which was 1-2(Cosx)^2, and multiplying r^2 on both sides, but I didn't get anywhere. Help, please?

1. amistre64

r = 1- cos(2x) correct?

2. amistre64

r^2 = r - r cos(2x) right?

3. amistre64

cos(2x) = cos^2 - sin^2

4. amistre64

maybe better like this: r = 1 - (cos^2(x) - sin^2(x)) r = 1 - cos^2(x) + sin^2(x) r = 1 -cos^2 + (1 - cos^2) r = 2 - 2 cos^2 r/2 = = 1- cos^2 r/2 = sin^2

5. amistre64

any luck with this? :)

6. mathmagician

correct answer is $(x^2+y^2)^3=4y^4$ rewrite the equation $r=1-\cos(2t)$ to $r=2\sin^2(t)$ and use identities: $r^2=x^2+y^2 and \sin(t)=y/r$