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Polar Coordinates: Tangents to Polar Curves

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First published at 05:34 UTC on January 16th, 2018.

Math Easy Solutions

MES

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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 Steemit: https://steemit.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
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 .