Question

r=2sin2(theta)
I'm supposed to convert it into rectangular form. I know mostly how to do it but I'm puzzled because there is a two in front of theta?

Answer 1

Is it sin^2(theta) or sin (2theta)?

Answer 2

Okay so you know that \[r = \sqrt{ x^{2}+y ^{2}}\] and \[\theta = \tan^{-1} (y/x)\]. So \[x = rcos(\theta)\] and \[y = rsin(\theta)\]. So if \[r = 2\sin^{2}(\theta) \] then square both sides and get that \[r^2 = 4\sin^{4}(\theta)\], which means\[x^2+y^2 = 4y^4/ (x^4+y^4)\] . If its\[r = 2\sin(2\theta)\], use the double angle formula for cosines to separate it into two functions of theta and then solve using the substitutions given