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

1 Answer
George C.
Dec 27, 2015

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

#r = 5#

Explanation:

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#

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