Area in Polar Coordinates

Find the area it encloses.
r = 5cos(θ)

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  1. What are the limits of theta? How do you deal with negative r from theta = 90 to 270 degrees?

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  2. Isn't that just a circle with diameter from (0,0) to (5,0) ?
    area would be π(5/2)^2 = 25π/4

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  3. We know from converting from polar to rectangular ...
    r √(x^2 + y^2) , x = rcosØ , and y = rsinØ

    so
    rcosØ = x
    cosØ = x/r
    5cosØ = 5x/r

    and

    √(x^2 + y^2) = 5x/(√(x^2 + y^2))
    cross-multiply
    x^2 + y^2 = 5x

    which is a circle as described in previous reply.

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