How do you convert r= -8(cos(x)-(sin(x)) r=−8(cos(x)−(sin(x)) into cartesian form?

1 Answer
A. S. Adikesavan
Apr 13, 2016

Taking x to mean the polar co-ordinatethetaθ, the cartesian form is
x^2+y^2+8x-8y=0x2+y2+8x−8y=0.

Explanation:

Use costheta=x/r, sintheta=y/r and r^2=x^2+y^2cosθ=xr,sinθ=yrandr2=x2+y2.
The result is
x^2+y^2+8x-8y=0x2+y2+8x−8y=0 or (x+4)^2+(y-4)^2=32(x+4)2+(y−4)2=32.
This represents the circle, with center at (-4, 4) and radius=sqrt32=4sqrt2(−4,4)andradius=√32=4√2

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