pre calculus
posted by Meredith
in the equation (x4)^2+y^2=16 the letters x and y represent rectangular coordinates. Write the equivalent equation using polar coordinates. solve for r

Reiny
from your previous question, recall
sinØ = y/r > y = rsinØ
cosØ = x/r > x = rcosØ
(x4)^2+y^2=16
(rcosØ 4)^2 + r^2sinØ = 16
r^2 cos^2  8rcosØ + 16 + r^2sin^2 Ø = 16
r^2 (cos^2 Ø + sin^2 Ø)  rcosØ + 16 = 16
r^2 rcosØ = 0
r  cosØ = 0
check:
http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+cos%C3%98
http://www.wolframalpha.com/input/?i=plot+(x4)%5E2%2By%5E2%3D16 
Steve
Clearly the graph is a circle of radius 4 with center at (4,0).
You know that r = cosθ is a circle with radius 1/2 and center at (0,1/2).
so, we have r = 8cosθ 
Reiny
Steve has the correct equation.
I don't know why my 8 was dropped in my 3rd last line, just careless.
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