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Polar Coordinates: Area: Example 2: Cardioid and Circle

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First published at 21:21 UTC on December 24th, 2017.

Math Easy Solutions

MES

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In this video I go over another example on calculating the area of polar curves and this time find the area enclosed by a circle yet separated by a cardioid. The Cardioid, or Heart in Greek, is the same formula I had previously graphed in my earlier example video. To save time, I plot both of the graphs together by using the Desmos calculator to obtain the resulting area we need to calculate. The first step in solving for the area is to find the points at which they intersect. From there we can apply the formula for the area of a polar curve which I covered in my earlier video, but this time we solve for the area of a polar circle, and then subtract from it the area of the polar cardioid. This is a very important video in understanding how to go about solving in detail the area enclosed by two polar curves, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvVAKCYLCqdXeyXJow

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-area-example-2-cardioid-and-circle

Related Videos:

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
Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY
Half Angle Trigonometry Identities: http://youtu.be/0bY6tHZhBSI .

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