Question

How do you convert `y=x^2` into a polar equation?

Answer 1

`r = tanthetasectheta`

Explanation:

using the links between Cartesian and Polar coordinates.

`• x = rcostheta`

`• y = r sintheta`

We can now write the above equation as :

`r sintheta = ( r costheta )^2 = r^2 cos^2theta`

(dividing both sides by r )

`( rsintheta)/r = (r^2cos^2theta)/r`

`sintheta = rcos^2theta`

`rArr r = sintheta/costheta xx 1/costheta = tantheta sectheta`