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## Calculus 2

### Unit 5: Lesson 9

Arc length: polar curves

# Worked example: Arc length of polar curves

What is the arc length of the polar curve r = 4sin(theta)?

## Want to join the conversation?

• For Pi/2<Theta<Pi and 3Pi/2<Theta<2Pi, the value of r is negative. Do you mean r=Absolute value(4*sin(2Theta))?
(1 vote)
• It does not matter if it is negative or not, because the values will get squared, which means that it will always be positive.

And another fact about r, is that when you are sketching the graph, the negative r values will transform into positive values, but in the opposite direction. This is why polar graphs look so pretty and why r(theta) is a function, even though it looks like it will not pass a vertical line test. If you look at the function definition, it's clear that for every theta there is only one r, so r(theta) is indeed a function.
• We can’t use calculators on tests :-( (sad face)
(1 vote)
• Mostly because teachers don't want you to cheat. ;-) (winking face)
(1 vote)
• The expression does convert into sqrt(24cos(4theta)+40) using the double-angle identity, but that is still troublesome to do out.