Polar Coordinates: Example 9: Cardioid: Part 4


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    Published on Oct 08, 2022
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    In this video I over Part 4 of Example 9 on Polar Coordinates and this time revisit the slope formula I derived in Part 1 to show that it can be solved in a simpler way. The curve we are given is the polar curve r = 1 + sinϴ, when we derive the formula for the slope of a tangent line to that curve it is important to note that the way we go about solving it early on can greatly affect the “appearance” of the final answer. This is because when working with trigonometric functions we need to understand that there are many different trig identities we can use, and also use to simplify the final result. In this part I show that by simply replacing r with 1 + sinϴ in the parametric equations for x and y obtained from Part 1, we can get a simpler “looking” final result. This result is in fact the same in terms of value as in Part 1, and I prove that by re-arranging the result using trig identities. This is a very useful video in showing how we can save time by simplifying the equations at the start of any calculation which deals with trigonometry, so make sure to watch this video!

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    View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-example-9-cardioid-part-4

    Related Videos:

    Polar Coordinates: Example 9: Cardioid: Part 3: Question B: https://youtu.be/-TZHaTjHfb8
    Polar Coordinates: Example 9: Cardioid: Part 2: Question A: https://youtu.be/gUYmzZ8Cfhg
    Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra: https://youtu.be/MlIhueP36EE
    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 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
    Trigonometric Identity: sin(2x) = 2sin(x)cos(x): http://youtu.be/IaZFDmVtyyU
    Trigonometric Identity: cos(2x) = 1 - 2sin2(x): http://youtu.be/XGk2CpbEl8I .

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