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Math Help - Find all points of intersection

  1. #1
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    Find all points of intersection

    I'm asked to find all points of intersection between

    r=1-\cos{\theta} and
    r=1+\sin{\theta}.

    I've graphed both polar equations. The first one looks like a heart rotated 90 degrees to the right. The second like a heart flipped vertically.

    I know that I'm supposed to set the equations equal to each other:

    1-\cos{\theta} = 1+\sin{\theta}

    \cos{\theta} + \sin{\theta} = 0

    So, I need something that either makes both cos and sin zero, or makes them opposites of each other.

    So, \theta = \frac{3\pi}{4}. But now that I have that, I'm not really sure how to proceed. Do I integrate one of the functions from 0 to \frac{3\pi}{4}?

    Confused...
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  2. #2
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    Re: Find all points of intersection

    Quote Originally Posted by centenial View Post

    \cos{\theta} + \sin{\theta} = 0

    So, I need something that either makes both cos and sin zero, or makes them opposites of each other.
    \cos{\theta} + \sin{\theta} = 0

    -\cos{\theta} = \sin{\theta}

    -1 = \frac{\sin{\theta}}{\cos{\theta}}

    -1 = \tan{\theta}

    Solve this? Then sub in for r
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  3. #3
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    Re: Find all points of intersection

    Quote Originally Posted by centenial View Post
    I'm asked to find all points of intersection between

    r=1-\cos{\theta} and
    r=1+\sin{\theta}.

    I've graphed both polar equations. The first one looks like a heart rotated 90 degrees to the right. The second like a heart flipped vertically.

    I know that I'm supposed to set the equations equal to each other:

    1-\cos{\theta} = 1+\sin{\theta}

    \cos{\theta} + \sin{\theta} = 0

    So, I need something that either makes both cos and sin zero, or makes them opposites of each other.

    So, \theta = \frac{3\pi}{4}. But now that I have that, I'm not really sure how to proceed. Do I integrate one of the functions from 0 to \frac{3\pi}{4}?

    Confused...
    What has integration got to do with the question as posted.
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