SOLUTION: please, someone should help me. Here is the question. Transform this equation from polar coordinate to rectangular coordinate. r= 3 raise to the power theta. Thanks. I tried to mul

Algebra ->  Test  -> Lessons -> SOLUTION: please, someone should help me. Here is the question. Transform this equation from polar coordinate to rectangular coordinate. r= 3 raise to the power theta. Thanks. I tried to mul      Log On


   

Question 784568: please, someone should help me. Here is the question. Transform this equation from polar coordinate to rectangular coordinate. r= 3 raise to the power theta. Thanks. I tried to multiply thru by r so that i can substitute r^2 for x^2 +y^2 but how to manipulate the side is the problem.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Convert the polar equation
given: r=+3%5E%28theta%29

to rectangular form.
Solution :


r=+3%5E%28theta%29....multiply both sides by r
r%2Ar=+r%2A3%5E%28theta%29
r%5E2=+r%2A3%5E%28theta%29+

We now use the relationship between polar and rectangular coordinates:
r%5E+2+=+x+%5E2+%2B+y%5E+2 and y+=+r%2A3%5E%28theta%29 to rewrite the equation as follows:
+x%5E2+%2B+y+%5E2+=+r%2A3%5E%28theta%29
x%5E+2+%2B+y+%5E2+-+y++=+0....complete the square
x%5E+2+%2B+y+%5E2+-+y%2B1%2F4-1%2F4++=+0
x%5E+2+%2B+%28y++-1%2F2%29%5E2++=+1%2F4 or
%28x-0%29%5E+2+%2B+%28y++-1%2F2%29%5E2++=+%281%2F2%29%5E2
so, it is the equation of a circle with
center: ( +0+,1%2F2)
radius: 1%2F2