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 Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-9-cardioid-part-4
Related Videos:
Polar Coordinates: Example 9: Cardioid: Part 3: Question B:
Polar Coordinates: Example 9: Cardioid: Part 2: Question A:
Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra:
Polar Coordinates: Tangents to Polar Curves:
Polar Coordinates: Symmetry:
Polar Coordinates: Example 8: Four-Leaved Rose:
Polar Coordinates: Example 7: Cardioid:
Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian:
Polar Coordinates: Example 5: Straight Lines:
Polar Coordinates: Example 4: Circle:
Polar Coordinates: Example 3: Cartesian to Polar
Polar Coordinates: Example 2: Polar to Cartesian:
Polar Coordinates: Cartesian Connection:
Polar Coordinates: Example 1:
Polar Coordinates:
Parametric Equations and Polar Coordinates:
Trigonometric Identity: sin(2x) = 2sin(x)cos(x):
Trigonometric Identity: cos(2x) = 1 - 2sin^2(x): .
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I don’t always solve for the slope of a tangent line to polar curve but when I do I usually show how we can do it in a simpler way ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-9-cardioid-part-4