Question

Find the length of the arc on the unit circle with the given central angles

a. 315º

b. 240º

Answer 1

$Since\:it\:is\:a\:unit\:circle\:its\:radius\:is\:one\:unit$.

$The\:circumfrence\:2\pi r\:is\:simplified\:to\:2\pi .$

$\left(a\right)\:\:\frac{arc\:length}{circumfrence}=\frac{central\:angle}{360^{\circ }}$

$\frac{arc\:length}{2\pi }=\frac{315^{\circ }}{360^{\circ }}$

$arc\:length=\frac{315\times2\pi }{360}$

$arc\:length=\frac{7}{4}\pi$

$\left(b\right)\:\:\frac{arc\:length}{circumfrence}=\frac{central\:angle}{360^{\circ }}$

$\frac{arc\:length}{2\pi }=\frac{240^{\circ }}{360^{\circ }}\:$

$\:arc\:length=\frac{240\times2\pi }{360}$

$arc\:length=\frac{4}{3}\pi$