How do you convert $rcos(t) = 4$ into a rectangular equation?

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Answer 1 · 2018-07-13T20:53:27

$x=4$

Consider a point $P$ with rectangular coordinates $(x,y)$ and polar coordinates $(r,theta)$ :

![ jwilson.coe.uga.edu )

As we can see in the diagram above, we can state some relations between the rectangular and polar coordinates:

$costheta = x/r => x=rcostheta$

$sintheta=y/r => x=rsintheta$

$x^2+y^2=r^2$

It is worth to note that the name of the angle variable does not matter; calling it $t$ is equivalent to calling it $theta$ . As such, the function

$rcost=4$

is equivalent to saying

$x=4$

in rectangular form.

How do you convert rcos(t) = 4rcos(t) = 4 into a rectangular equation?