Polar Coordinates: Arc Length: Example 1: Cardioid


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    Published on Jul 29, 2021
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    In this video I go over a quick example on using the arc length formula derived in my earlier video for polar curves, and this time find the length of the cardioid r = 1 + sinϴ. This is the same cardioid that I graphed in my earlier video titled Polar Coordinates: Example 7: Cardioid. Solving for the arc length is pretty standard for the cardioid (Greek for “heart”), as we just plug in the variables into the arc length formula. The resulting integral involves integrating the trigonometric function (2+2sinϴ)1/2 which is tedious to solve and thus I just used an online integral calculator to solve it. I may solve the integral by hand in a later video so stay tuned! The result of the calculator is that the cardioid has a length of 8, which is a very simple and neat result. This is a useful and quick video to show you how to use the arc length formula so make sure to watch the video!

    Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvd_hYKUOCPlKNkVMA

    View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-arc-length-example-1-cardioid

    Related Videos:

    Polar Coordinates: Arc Length Formula: https://youtu.be/lrh15Brq9B4
    Polar Coordinates: Area Formula: Area Between Two Polar Curves: https://youtu.be/bAbz1T-_Twc
    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
    Trigonometry Identities: Proof that sin2(x) + cos2(x) = 1: http://youtu.be/o-fAx_96lgw
    Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY .

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