How do you convert $r = 2/(3cos(θ)-sin(θ))$ into a rectangular equation?

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Answer 1 · 2015-11-25T22:34:06

First, use the following identities ...

Next, use these two identities and substitute above:

$x=rcostheta$
$y=rsintheta$

After substituting and simplify ...

$r=(2)/(3costheta-sintheta)$

$r=(2)/(3x/r-y/r)=(2r)/(3x-y)$

Next, divide both sides by r:

$1=(2)/(3x-y)$

Now that everything is in terms of $x or y$ , simplify one more time:

$y=3x-2$

A straight line with slope 3 and y-intercept equal to -2.

hope that helped

How do you convert r = 2/(3cos(θ)-sin(θ)) r = 2/(3cos(θ)-sin(θ)) into a rectangular equation?