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 Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-arc-length-formula
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Parametric Equations and Polar Coordinates:
Parametric Calculus: Arc Length Part 1:
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I don't always derive the arc length formula for polar curves but when I do I usually build upon the arc length formula in parametric form ;)
View Video Notes: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-arc-length-formula
Ive learned this during my review :) together with the pappus preposition.