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Cartesian Equations-finding arc length

https://www.quora.com/profile/Bravewarrior/p-147186485
Here is the question and its solution. I am stuck on part c. Can someone please explain how they got theta as the value shown in the solution? Thanks!
Reply 1
Its a circle of radius 9 between the angles -pi/6 and pi/2. So the arc length is
9*(pi/2 + pi/6)
Original post by mqb2766
Its a circle of radius 9 between the angles -pi/6 and pi/2. So the arc length is
9*(pi/2 + pi/6)

Thank you! I was struggling to understand it visually, but I guess you just have to look at the given restriction/interval?
Reply 3
Original post by pigeonwarrior
Thank you! I was struggling to understand it visually, but I guess you just have to look at the given restriction/interval?

The "t" parametric varaible corresponds to the angle "theta". Its the central idea in the question about describing a circle parametrically so roughly
x = r*cos(t)
y = r*sin(t)
(with a translation / nonzero centre) rather than cartesian
x^2+y^2=r^2

Parts a) and b) are all about making you view it as a circle, then the arc length should be straightforward.
(edited 3 months ago)
Original post by mqb2766
The "t" parametric varaible corresponds to the angle "theta". Its the central idea in the question about describing a circle parametrically so roughly
x = r*cos(t)
y = r*sin(t)
(with a translation / nonzero centre) rather than cartesian
x^2+y^2=r^2

Parts a) and b) are all about making you view it as a circle, then the arc length should be straightforward.

Yup, that makes sense 🙂 thank you!

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