How do you write the polar equation $r = 3 cos θ$ $r=3costheta$ in rectangular form?

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Answer 1 · 2018-06-01T08:02:21

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$r = 3 cos θ$ $r = 3 cos theta$

$\Rightarrow r^{2} = 3 r cos θ$ $=> r^2 = 3 r cos theta$

Use your conversions:

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

$r cos θ = x$ $r cos theta = x$

$r sin θ = y$ $r sin theta = y$

$\Rightarrow x^{2} + y^{2} = 3 x$ $color(red)(=> x^2+ y^2 = 3x$

You can also put this into the regular circle form

$\Rightarrow x^{2} - 3 x + \frac{9}{4} + y^{2} = \frac{9}{4}$ $=> x^2 - 3x + 9/4 + y^2 = 9/4$

$\Rightarrow {(x - \frac{3}{2})}^{2} + y^{2} = \frac{9}{4}$ $color(red)(=> (x - 3/2 )^2 + y^2 = 9/4$

How do you write the polar equation r=3costhetar=3cosθr=3costheta in rectangular form?