How do you convert $5 x = 5 y$ $5x=5y$ to polar form?

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Answer 1 · 2016-10-13T10:36:21

$5 x = 5 y$ $5x=5y$ in polar form is $θ = \frac{π}{4}$ $theta=pi/4$

Relation between Cartesian coordinates $(x, y)$ $(x,y)$ and polar coordinates $(r, θ)$ $(r,theta)$ is given by

$x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$

Hence $5 x = 5 y$ $5x=5y$ in polar form can be written as

$5 r cos θ = 5 r sin θ$ $5rcostheta=5rsintheta$

or $cos θ = sin θ$ $costheta=sintheta$

or $tan θ = 1$ $tantheta=1$

How do you convert 5x=5y5x=5y5x=5y to polar form?