Trig/pre-calc

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r=8cos(theta)+5sin(theta), convert the polar equation into a rectangular equation and then complete the square and determine the center radius...?

Help?! I missed the section, and am not getting anywhere with the text...

  • Trig/pre-calc -

    In your text, you should find a diagram similar to this one
    http://en.wikipedia.org/wiki/File:Polar_to_cartesian.svg

    If you label the endpoint of the rotating arm as either
    (x,y) in rectangular and (r,Ø) in polar, then

    x = rcosØ or cosØ = x/r
    y = rsinØ or sinØ = y/r

    also x^2 + y^2 = r^2, and tanØ = y/x

    then in your equation r = 8(x/r) + 5(y/r)
    multiply by r
    r^2 = 8x + 5y
    x^2 + y^2 = 8x + 5y
    x^2 - 8x + y^2 - 5y = 0

    This is the equation of a circle. I will assume you know how to complete the square and thus find the centre and radius.

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