Question

How do you convert `r = 2cos2θ` into rectangular form?

Answer 1

Use these identities:
`x=rcostheta`
`y=rsintheta`
`r^2=x^2+y^2`
`cos2theta=cos^2theta -sin^2theta`

Explanation:

`r=2cos2theta=2[cos^2theta -sin^2theta]`

Now, further simplification using the identities ...

`r=2/r^2(x^2-y^2)=[2(x^2-y^2)]/(x^2+y^2)`

`sqrt(x^2+y^2)=[2(x^2-y^2)]/(x^2+y^2)`

`(x^2+y^2)^(3/2)-2(x^2-y^2)=0`

hope that helps