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In this video I go over a quick example on using the arc length formula derived in my earlier video for polar curves, and this time find the length of the cardioid r = 1 + sinϴ. This is the same cardioid that I graphed in my earlier video titled Polar Coordinates: Example 7: Cardioid. Solving for the arc length is pretty standard for the cardioid (Greek for “heart”), as we just plug in the variables into the arc length formula. The resulting integral involves integrating the trigonometric function (2+2sinϴ)<sup>1/2</sup> which is tedious to solve and thus I just used an online integral calculator to solve it. I may solve the integral by hand in a later video so stay tuned! The result of the calculator is that the cardioid has a length of 8, which is a very simple and neat result. This is a useful and quick video to show you how to use the arc length formula so make sure to watch the video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvd_hYKUOCPlKNkVMA

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-arc-length-example-1-cardioid

Related Videos: 

Polar Coordinates: Arc Length Formula: [https://youtu.be/lrh15Brq9B4](https://youtu.be/lrh15Brq9B4)
Polar Coordinates: Area Formula: Area Between Two Polar Curves: [https://youtu.be/bAbz1T-_Twc](https://youtu.be/bAbz1T-_Twc)
Polar Coordinates: Area Formula: [https://youtu.be/wd-EwiKzqa0](https://youtu.be/wd-EwiKzqa0)
Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: [https://youtu.be/xY9Be9HHRsk](https://youtu.be/xY9Be9HHRsk)
Polar Coordinates: Cartesian Connection: [https://youtu.be/HcaTYrpmGaU](https://youtu.be/HcaTYrpmGaU)
Polar Coordinates: [https://youtu.be/-KAdZL-N4ok](https://youtu.be/-KAdZL-N4ok)
Parametric Equations and Polar Coordinates: [https://youtu.be/usSors49Gdw](https://youtu.be/usSors49Gdw)
Trigonometry Identities: Proof that sin<sup>2</sup>(x) + cos<sup>2</sup>(x) = 1: [http://youtu.be/o-fAx_96lgw](http://youtu.be/o-fAx_96lgw)
Polar Coordinates: Example 7: Cardioid: [https://youtu.be/rPErcaqNUIY](https://youtu.be/rPErcaqNUIY) .

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