Question

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

$r=a\sin \theta +b\cos \theta ,\mathrm{where}a\mathrm{and}b\mathrm{are}\mathrm{positive}\mathrm{constants}\mathrm{for}\theta \in [0,\pi ]$

Short answer

The arc length is$2\sqrt{\left(a^2+b^2\right)}\mathrm{\pi }\mathrm{units}$

Step-by-step solution

Given information.

The curve is$r=a\sin \theta +b\cos \theta ,\mathrm{where}a\mathrm{and}b\mathrm{are}\mathrm{positive}\mathrm{constants}\mathrm{for}\theta \in [0,\pi ]$

Arc length.

The length of an arc is given by,