How do you graph $r = 3 + 3 cos θ$ $r=3+3costheta$ on a graphing utility?

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Answer 1 · 2017-10-25T20:02:19

Convert to rectangular form:

$x^{2} + y^{2} = 3 \sqrt{x^{2} + y^{2}} + x$ $x^2+y^2=3sqrt(x^2+y^2)+x$

Given:

$r = 3 + 3 cos θ$ $r = 3+3cos theta$

Convert from polar to rectangular coordinates using:

$r = \sqrt{x^{2} + y^{2}}$ $r = sqrt(x^2+y^2)$

$x = r cos θ$ $x = r cos theta$

So multiplying the given equation by $r$ $r$ we find:

$x^{2} + y^{2} = r^{2} = 3 r + 3 r cos θ = 3 \sqrt{x^{2} + y^{2}} + x$ $x^2+y^2 = r^2 = 3r+3r cos theta = 3sqrt(x^2+y^2) + x$

So we can put the equation:

$x^{2} + y^{2} = 3 \sqrt{x^{2} + y^{2}} + x$ $x^2+y^2=3sqrt(x^2+y^2)+x$

into our graphing utility to get:

graph{x^2+y^2=3sqrt(x^2+y^2)+x [-10, 10, -5, 5]}

Note carefully that this is not a circle.

How do you graph r=3+3cosθr=3+3costheta on a graphing utility?