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