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The arc length of polar functions: Find the arc lengths of the following polar functions.r=acosθ

, where is a positive constant, for

Short Answer

Expert verified

The arc length is2aπunits

Step by step solution

01

Given information.

r=acosθandθ0,2π

02

Arc length.

The length of an arc is given by,

L=αβr2+drdθ2dθ

So,

role="math" localid="1662989532460" L=02πa2cos2θ+-asinθ2dθdrdθ=-asinθ=02πa2cos2θ+a2sin2θdθ=02πadθcos2θ+sin2θ=1=2aπ-0=2aπunits

Thus, the arc length is2aπunits

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