# What is the arclength of the polar curve #f(theta) = cos^2theta-3sin^2theta # over #theta in [pi/3,pi/2] #?

Arclength is given by:

Expand the square and combine terms:

Complete the square in the square root:

Factor out the larger piece:

Apply binominal expansion:

Simplify:

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The arc length of the polar curve ( f(\theta) = \cos^2(\theta) - 3\sin^2(\theta) ) over the interval ( \theta ) in ( \left[\frac{\pi}{3}, \frac{\pi}{2}\right] ) is ( \frac{\sqrt{10}}{3} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the arclength of the polar curve #f(theta) = sin(3theta)-4cot6theta # over #theta in [0,pi/4] #?
- How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3costheta#?
- What is the distance between the following polar coordinates?: # (2,(12pi)/8), (1,(-pi)/8) #
- What is the polar form of #( 36,48 )#?
- What is the polar form of #( -4,-2 )#?

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