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

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Answer 1 · 2018-01-05T21:19:40

$theta = pi/2$

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

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

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