Example: Determine the length of the arc of a circle with a radius of 6cm if the arc formed is subtended by an angle of \(234^\circ\). Give an exact answer.
Solution To answer this question we will first convert the degrees to radians:
\[ \solve{ 234\times\dfrac{\pi}{{180}}&=&\dfrac{234\pi}{{180}}\\&=&\dfrac{13\pi}{{10}} } \]Next, we will use the arc length formula, \(s=r\theta\), to calculate the exact length.
\[ \solve{ s&=&6\times\dfrac{13\pi}{{10}}\\ s&=&\dfrac{39\pi}{{5}}\text{ cm} } \]And now we have our exact answer for the length of the arc subtended by the angle given.