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in the equation r= 5/(sin theta +2cos theta) the letters r and theta represent polar coordinates. Write the equivalent equation using rectangular coordinates.

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1 answer

  1. recall:
    sinØ = y/r and cosØ = x/r

    so:
    r= 5/(sin theta +2cos theta)
    r = 5/(y/r + 2x/r)
    r = 5/((2x+ y)/r)
    r = 5r/(2x + y)
    1 = 5/(2x+y)
    2x + y = 5 <----- a straight line

    proof:
    http://www.wolframalpha.com/input/?i=polar+plot+r%3D+5%2F(sin+theta+%2B2cos+theta)

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