How do you convert $x^2 + y^2 = 25$ into polar form?

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Answer 1 · 2015-12-27T13:23:21

Substitute $x = r cos theta$ and $y = r sin theta$ into the equation, then simplify to find:

$r = 5$

Substitute $x = r cos theta$ and $y = r sin theta$ into the equation:

$25 = x^2+y^2$

$=(r cos theta)^2 + (r sin theta)^2$

$=r^2 cos^2 theta + r^2 sin^2 theta$

$=r^2( cos^2 theta + sin^2 theta)$

$=r^2$

since $cos^2 theta + sin^2 theta = 1$ for any $theta$

So $r^2 = 25$ , but we can assume $r > 0$ , hence:

$r = sqrt(25) = 5$

How do you convert x^2 + y^2 = 25x^2 + y^2 = 25 into polar form?