How do you convert $r=2sin theta + cos theta$ into rectangular form?

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Answer 1 · 2017-02-25T16:29:14

The equation is $(x-1/2)^2+(y-1)^2=5/4$

To convert from polar coordinates $(r, theta)$ to rectangular coordinates $(x,y)$ , we use the following equations

$x=rcostheta$ , $=>$ , $costheta=x/r$

$y=rsintheta$ , $=>$ , $sintheta=y/r$

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

Therefore,

$r=2sintheta+costheta$

$r=2*y/r+x/r$

$r^2=2y+x$

$x^2+y^2=2y+x$

$x^2-x+y^2-2y=0$

$x^2-x+1/4+y^2-2y+1=1+1/4$

$(x-1/2)^2+(y-1)^2=5/4$

This is the equation of a circle, center $(1/2,1)$ and radius $=sqrt5/2$

How do you convert r=2sin theta + cos thetar=2sin theta + cos theta into rectangular form?