In this video I go over another example on sketching polar coordinates and this time sketch the curve r = 1 + sinθ. Unlike in my previous example, instead of plotting points, I instead first sketch the curve on a Cartesian coordinate system and then from there transcribe the curve onto a polar coordinate system. Because the function r = 1 + sinθ is simply sinθ but shifted upwards by 1 on a Cartesian plane, it is easy to determine the points and how the shape would look like on a polar plane. I show in this video step by step how to go about graphing the function on polar coordinates through 4 intervals from θ = 0 to θ = 2pi. Outside of this range, the same path just gets traced over again because of the cyclical nature of the trigonometric function. The shape we end up having is in the shape of a heart, and is known as a Cardioid, which is in fact Greek for the word “heart”. This is a very useful video in showing the steps to follow to systematically graph a circular or trigonometric polar function, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvBqiGxa0hYLmBxy9g
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-example-7-cardioid
Related Videos:
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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I wish you and your family a Merry Christmas and Prosperous happy new year!
Thanks! And same to you and yours, Merry Christmas and Happy New Year!!
I don’t always sketch a Cardioid polar function but when I usually first sketch it on Cartesian Coordinates first ;)
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-example-7-cardioid