Question

How do you write the equation y=x in polar form?

Answer 1

`theta = pi/2`

Explanation:

We must use our polar co-ordinates knowledge:

`color(red)(r^2 = x^2 + y^2`

`color(red)(x = rcos theta`

`color(red)(y = rsintheta`

So hence `y = x` :

`rsintheta = r costheta`

`sintheta = costheta`

This yields the soution

`color(blue)(=> theta = pi/4`

In general

`color(orange)("Cartesian" : y = mx`

`color(orange)("Polar" : theta = tan^(-1) (m)`