In this video I go over an example on determining the arc length of a parametric curve and in this case look at the unit circle that is written in the parametric form: x = cos(t), y = sin(t), where t is between 0 and 2*pi. This is the same parametri…
In this video I go over an example on determining the arc length of a parametric curve and in this case look at the unit circle that is written in the parametric form: x = cos(t), y = sin(t), where t is between 0 and 2*pi. This is the same parametric curve which I have gone over in my earlier video, so make sure to watch that below to see how it is indeed a unit circle. When we apply the arc length formula to determine the arc length, we are in fact solving for the circumference of a circle with radius 1. Thus as expected the arc length is 2*pi. This is a fascinating result because it shows how we can use already well known mathematical properties as ways to confirm that our arc length formula is in fact correct. This is an important video to see how to apply the arc length formula to determine the length of a parametric curve, so make sure to watch this video!
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Related Videos:
Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ
Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM
Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Parametric Curves: Example 2: Unit Circle: https://youtu.be/SBkzZDlqTTE
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw .
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