How do you convert $r = 3 cos (θ)$ $r = 3cos(theta)$ into cartesian form?

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Answer 1 · 2015-11-22T21:00:49

Use the identities:

$r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$
$x = r cos θ$ $x=rcostheta$

First, multiply the equation by r:

$r^{2} = 3 (r cos θ)$ $r^2=3(rcostheta)$

Now, substitute the identities:

$x^{2} + y^{2} = 3 x$ $x^2+y^2=3x$

$x^{2} + y^{2} - 3 x = 0$ $x^2+y^2-3x=0$

A circle with radius 1.5 and center $(1.5, 0)$ $(1.5,0)$

hope that helped

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How do you convert r = 3cos(theta)r=3cos(θ)r = 3cos(theta) into cartesian form?