How do you find the exact length of the polar curve r=3sin(theta) on the interval 0 le theta le pi/3?

Custodio88j

Custodio88j

Answered question

2023-02-13

How to find the exact length of the polar curve r = 3 sin ( θ ) on the interval 0 θ π 3 ?

Answer & Explanation

Amaqumrhund1

Amaqumrhund1

Beginner2023-02-14Added 9 answers

The arc length is π .
Let's go over some specifics.
r = 3 sin θ
by differentiating with respect to θ ,
d r d θ = 3 cos θ
Therefore, the arc length L can be found by
L = 0 π 3 r 2 + ( d r d θ ) 2 d θ
= 0 π 3 3 2 sin 2 θ + 3 2 cos 2 θ d θ
by pulling 3 out of the square-root,
= 3 0 π 3 sin 2 θ + cos 2 θ d θ
by sin 2 θ + cos 2 θ = 1 ,
= 3 0 π 3 d θ = 3 [ θ ] 0 π 3 = 3 ( π 3 - 0 ) = π

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?