Polar Coordinates: Example 8: Four-Leaved Rose

Math Easy Solutions

description

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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