Polar Coordinates: Tangents to Polar Curves

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    mes

    Published on Nov 12, 2022
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    In this video I go over further into Polar Coordinates and this time illustrate how to solve for tangents to polar curves. In order to find the tangent line of a polar curve, we need to first covert the polar curve into parametric equation form in order to calculate the derivative. We can do this easily by using trigonometry and letting ϴ be the parameter. From here we can apply the derivative formula in parametric form, which I covered in my earlier videos on parametric calculus, as well as using the Product Rule to determine calculate the slope of the tangent line. I also show how the slope of the tangent lines at the origin, or pole, simplifies to tanϴ and since it is at the origins, the equation of any line through the origin will just be y = tan(ϴ)*x since tanϴ is just the slope. I also illustrate the slopes at the origins by revisiting Example 8 on polar coordinates on the 4-leaved rose curve. This is a very useful video in understanding to how calculate the slope of a polar curve by using parametric calculus, so make sure to watch this video!

    Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvMyYvBAVBQ1YJDhxg

    View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-tangents-to-polar-curves

    Related Videos:

    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 .


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