5

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!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvQO014ItCWPtaSNeg

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 - 2sin^{2}(x): http://youtu.be/XGk2CpbEl8I .

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