Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra

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    mes

    Published on Nov 05, 2022
    About :

    In this video I go over another example on Polar Coordinates, and this time look at revisiting the Cardioid, or Heart, example in my earlier video and determine the formula for the slope or tangent to the curve. This video goes over just determining the formula, in which I will solve the slopes in various cases and angles in later video so stay tuned for that. Determining the formula of the slope of a tangent line to the curve involves following the same method as in my last video on Tangents to Polar curves. Namely, first writing the polar curve equation into Parametric Equations and then apply the formula for the derivative using Parametric Calculus. Doing this we can a formula that involves many trigonometric terms, which I decided to simplify (because my Calculus book does so), and thus go over some pretty interesting factoring and trig algebra. This is a very interesting video into determining the slope of a polar curve, but even more so is the trigonometric algebra, so make sure to watch this video!

    Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvM_LvGHjQ4M00FUhw

    View video notes on the Hive blockchain: https://peakd.com/@mes/g8fcn-video-notes-polar-coordinates-example-9-cardioid-part-1-slope-formula-and-trigonometric-algebra

    Related Videos:

    Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY
    Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM
    Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE
    Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY
    Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE
    Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A
    Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs
    Polar Coordinates: Example 3: Cartesian to Polar: https://youtu.be/mV-9KTQM-RU
    Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU
    Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
    Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE
    Polar Coordinates: https://youtu.be/-KAdZL-N4ok
    Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
    Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
    Trigonometry Identities: Proof that sin2(x) + cos2(x) = 1: http://youtu.be/o-fAx_96lgw .


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