Polar Coordinates: Area: Example 3: Intersection Points

over 2 years ago (Edited)

In this video I go over a very important example on finding the intersection points of two polar curves, which is essential when determining the area bounded by two polar curves. This example involves finding the intersection points of the circle r = ½ and the four-leaved flower r = cos2ϴ. We can find 4 of these intersection points by setting the two equations equal to each other. But when we graph the curves using the amazing Desmos calculator, there are in fact 4 additional intersection points! This is because, as illustrated in my earlier video on the area bounded by two polar curves, the points of intersection can occur at different “times” or at different values of ϴ for each polar curve. But in this video I show that we can use symmetry of the curves to find the other 4 points, but also by noticing that the circle r = ½ can also be written as r = -1/2. Since r in polar coordinates is just the distance from the origin, whether r = +1/2 or -1/2 we get the same curve. When we set r = -1/2 equal to the flower r = cos2 ϴ and solve for the ϴ we in fact obtain the 4 additional intersection points. This is a very important video in that it illustrates the steps to take to find some of the intersection points of polar curves that are not so easy to solve, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvct1IpvRxEAQ5IpvA

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/6zxxy8-polar-coordinates-area-example-3-intersection-points

Related Videos:

Polar Coordinates: Area Formula: Area Between Two Polar Curves: https://youtu.be/bAbz1T-_Twc
Polar Coordinates: Area: Example 2: Cardioid and Circle: https://youtu.be/vSzxzNn3EiA
Polar Coordinates: Area: Example 1: r = cos 2ϴ: https://youtu.be/6kavQyGcODo
Polar Coordinates: Area Formula: https://youtu.be/wd-EwiKzqa0
Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw .

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