Question

How do I convert the polar equation `r=10 sin theta` to its Cartesian equivalent?

Answer 1

Cartesian coordinates, also known as Rectangular coordinates, are defined in terms of `x` and `y`. So, for this problem `theta` has to be eliminated/converted using basic foundations described by the unit circle and right triangle trigonometry.

`r=10sin(theta)`

Remember that ...

`x=r*cos(theta)`

`y=r*sin(theta)`

`r^2=x^2+y^2`

Multiply both sides of the equation by `r`

`r*r=10r*sin(theta)`

`r^2=10r*sin(theta)`

`x^2+y^2=10r*sin(theta)`

Use the fact that `y=r*sin(theta)` to make a substitution.

`x^2+y^2=10y`

`x^2+y^2-10y=0`

The above equation is the Cartesian/Rectangular coordinate equivalent to the given Polar equation.