Polar Coordinates: Arc Length Formula

over 2 years ago (Edited)

In this video I go over a quick derivation into the arc length formula for polar curves. The derivation involves using the already derived formula for arc length in parametric form, which I derived in my earlier videos, but then converting the polar curve into the well known pair of parametric equations: x = rcosϴ and y = rsinϴ. From here we can do some algebra and finally obtain the arc length formula which contains the derivative dr/dϴ and r within it. This is a very useful video for understanding how to build upon previous formulas, as well as for seeing how switching from polar and parametric equations is useful at times, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvdC4gEfj4_2mKeTSQ

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

Related Videos:

Polar Coordinates: Area Formula: Area Between Two Polar Curves: https://youtu.be/bAbz1T-_Twc
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
Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ
Trigonometry Identities: Proof that sin²(x) + cos²(x) = 1: http://youtu.be/o-fAx_96lgw .