Question

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?

Answer 1

r = 1- cos(2x) correct?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

any luck with this? :)

Answer 6

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:
\[r^2=x^2+y^2 and \sin(t)=y/r\]