Polar Coordinates: Area: Example 3: Intersection Points

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!

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View Video Notes on Steemit: https://steemit.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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