Answered: Arc Length in Polar Coordinates dx' L =…

Arc Length in Polar Coordinates dx' L = Remember: dt dt dt x =r cose For polar graphs: y =r sin 0 If we find derivatives and plug them into the formula, we (eventually) get: Length = {" * +() dr de

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter6: Trigonometric Functions: Unit Circle Approach

Section6.3: Trigonometric Graphs

Problem 90E: DISCUSS: Sinusoidal Curves The graph of y=sinx is the same as the graph of y=cosx shifted to the...

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Hello,

I am trying to solve for the arc length of polar graphs over an interval, and I have seen the two different equations that are shown in the attached picture. My math teacher only showed the first equation in lecture, but this picture shows that eventually you get the second equation if you solve using the first equation. If the r(theta) function is known, is it more efficient to start off with the second equation instead of the first?

Arc Length in Polar Coordinates
dx'
L =
Remember:
dt
dt
dt
x =r cose
For polar graphs:
y =r sin 0
If we find derivatives and plug them into the formula, we
(eventually) get:
Length = {" * +()
dr
de

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