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In this video I go over another example on sketching polar coordinate functions and this time sketch the curve r = cos2θ. Just like in my last example video, I show that we can first graph the function on a Cartesian coordinate system, and then systematically transcribe the curve onto a polar coordinate system. Doing so, we get a shape that looks like a 4-leaved rose, which is pretty cool! Also note, that I graphed the function for the domain of θ being between 0 and 2pi, but any other values we get the usual tracing over the same path because of the cyclical nature of the trigonometric cosine function. This example shows that a simple trigonometric function, when written in polar coordinates can create such amazing shapes, which was one of the main reasons that I started researching math in the first place! Polar coordinates (as well as parametric curves) are one of the coolest, and my personal favorite, math topics, and this video is an example of why, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvINFs-3GS1ygdVQNA
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-example-8-four-leaved-rose
Related Videos:
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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