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\(\displaystyle x^2+y^2=4\)

\(\displaystyle (r\cos(\theta))^2+(r\sin(\theta))^2=4\)

\(\displaystyle r^2\cos^2(\theta)+r^2\sin^2(\theta)=4\)

Factor the LHS...what do you have...is there a trig. identity you can apply?

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got it! thanks!

\(\displaystyle x^2+y^2=4\)

\(\displaystyle (r\cos(\theta))^2+(r\sin(\theta))^2=4\)

\(\displaystyle r^2\cos^2(\theta)+r^2\sin^2(\theta)=4\)

Factor the LHS...what do you have...is there a trig. identity you can apply?

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We see we have a circle centered at the origin, and in polar coordinates, that's simply a constant value for \(r\). The Cartesian equation:got it! thanks!

\(\displaystyle x^2+y^2=a^2\) where \(0<a\)

Has the polar equation:

\(\displaystyle r=a\)