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Math Help - areas in polar coordinates

  1. #1
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    areas in polar coordinates

    I have seen examples where the thetas are preset, but I have trouble with the ones where I have to find them.

    Find the area of the regions.

    1. Inside the oval limacon r = 4 + 2 cos(theta)

    I found the value for theta... -4 = 2cos(theta)

    -2 = cos(theta) -> arccos(-2) = theta... but the calc says this is undefined.

    Need help
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  2. #2
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    Quote Originally Posted by driver327 View Post
    I have seen examples where the thetas are preset, but I have trouble with the ones where I have to find them.

    Find the area of the regions.

    1. Inside the oval limacon r = 4 + 2 cos(theta)

    I found the value for theta... -4 = 2cos(theta) ??? r does not equal 0.

    -2 = cos(theta) -> arccos(-2) = theta... but the calc says this is undefined.

    Need help
    why are you trying to solve for \theta ?

    A = \int_0^{2\pi} \frac{(4+2\cos{\theta})^2}{2} \, d\theta = \int_0^{\pi} (4+2\cos{\theta})^2 \, d\theta<br />
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  3. #3
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    I did it like that and got the right answer!! my question is: for those types of problems, do I automatically assume that the parameters is 1 full rotation? (from 0 to 2pi or 0 to pi w/o the 1/2).. just trying to understand it
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  4. #4
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    Quote Originally Posted by driver327 View Post
    I did it like that and got the right answer!!

    not with the posted problem you didn't ... what problem are you talking about?

    my question is: for those types of problems, do I automatically assume that the parameters is 1 full rotation? (from 0 to 2pi or 0 to pi w/o the 1/2)
    some polar curves require \theta to run from 0 to 2\pi to get the full graph ... there are some that require less, like r = \sin(3\theta) ... it only need to run from 0 to \pi to get a complete graph.
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