Question

How do you convert `r=7sintheta` into rectangular equations?

Answer 1

`x^2+y^2-7y=0`

Explanation:

The relation between polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` is given by

`x=rcostheta`, `y=rsintheta` i.e. `x=r/costheta`, `y=r/sintheta` and `r^2=x^2+y^2`,

Hence `r=7sintheta` can be written as

`r=7sintheta` (multiplying both sides by `r`) or

`r^2=7rsintheta` or

`x^2+y^2=7y` or

`x^2+y^2-7y=0`

graph{x^2+y^2-7y=0 [-10.29, 9.71, -1.48, 8.52]}