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

r=secθforθπ6,π6

Short Answer

Expert verified

The arc length is23units

Step by step solution

01

Given information.

The given curve isr=secθforθπ6,π6

02

Arc length

The arc length of the curve is given by,

L=αβr2+drdθ2dθL=-π6π6secθ2+secθtanθ2dθdrdθ=secθtanθL=-π6π6sec2θ+sec2θtan2θdθL=-π6π6sec2θ1+tan2θdθsin2θ+cos2θ=1L=-π6π6sec2θsec2θdθ1+tan2θ=sec2θL=-π6π6sec2θdθL=tanθ-π6π6L=tanπ6-tan-π6L=tanπ6-π-tanπ6L=2tanπ6-πL=23units

The arc length isL=23units

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