Polar Coordinates: Area: Example 2: Cardioid and Circle


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    Published on Nov 29, 2021
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    In this video I go over another example on calculating the area of polar curves and this time find the area enclosed by a circle yet separated by a cardioid. The Cardioid, or Heart in Greek, is the same formula I had previously graphed in my earlier example video. To save time, I plot both of the graphs together by using the Desmos calculator to obtain the resulting area we need to calculate. The first step in solving for the area is to find the points at which they intersect. From there we can apply the formula for the area of a polar curve which I covered in my earlier video, but this time we solve for the area of a polar circle, and then subtract from it the area of the polar cardioid. This is a very important video in understanding how to go about solving in detail the area enclosed by two polar curves, so make sure to watch this video!

    Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvVAKCYLCqdXeyXJow

    View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-area-example-2-cardioid-and-circle

    Related Videos:

    Polar Coordinates: Area: Example 1: r = cos 2ϴ: https://youtu.be/6kavQyGcODo
    Polar Coordinates: Area Formula: https://youtu.be/wd-EwiKzqa0
    Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk
    Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
    Polar Coordinates: https://youtu.be/-KAdZL-N4ok
    Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
    Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY
    Half Angle Trigonometry Identities: http://youtu.be/0bY6tHZhBSI .

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