Sunday, March 27, 2022

March Calculus Madness Sweet Sixteen - Day 12: Arc Length of Sine and Cosine

 ------------


Welcome to March Calculus Madness!


------------


What is the arc length of y = sin x and y = cos x from x = 0 to x = 2 * π


The arc length of y(x) is calculated by:


∫ √(1 + (dy/dx)^2) dx for x = a to x = b


For y(x) = sin x, dy/dx = cos x, (dy/dx)^2 = cos^2 x


Arc length of y = sin x from x = 0 to x = 2*π

∫ √(1 + cos^2 x) dx for x = 0 to x = 2*π ≈ 7.64039557806


Likewise, for y(x) = cos x, dy/dx = -sin x, (dy/dx)^2 = sin^2 x

∫ √(1 + sin^2 x) dx for x = 0 to x = 2*π ≈ 7.64039557806


Yes, the arc lengths are the approximately the same.  


Eddie


All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.