Extension Test: Degrees, Radians, and Arc Length Solutions

If the problem is in degrees, convert it to radians using π. If the problem is in radians, convert it to degrees.

$\frac{4 π}{3}$

$d e g = r a d \cdot \frac{180}{π} \frac{4 π}{3} \cdot \frac{180}{π} = \frac{4 \cdot {180 π}^{60}}{3 π} = 240 °$

$215 °$

$r a d = d e g \cdot \frac{π}{180} 215 \cdot \frac{π}{180} = \frac{43 π}{36}$

$60 °$

$r a d = d e g \cdot \frac{π}{180} 60 \cdot \frac{π}{180} = \frac{π}{3}$

$\frac{7 π}{10}$

$d e g = r a d \cdot \frac{180}{π} \frac{7 π}{10} \cdot \frac{180}{π} = \frac{7 \cdot {180 π}^{18}}{10 π} = 126 °$

Determine the arc length of a circle with the given central angle and radius.

$48 °, r = 5$

$r a d = d e g \cdot \frac{π}{180} r a d = 48 \cdot \frac{π}{180} = \frac{4 π}{15} s = r θ s = 5 \cdot \frac{4 π}{15} s = \frac{4 π}{3}$

$r = \frac{1}{2}, s = \frac{2 π}{9}$

$s = r θ (2) \frac{2 π}{9} = \frac{1}{2} \cdot θ (2) θ = \frac{4 π}{9} d e g = r a d \cdot \frac{180}{π} d e g = \frac{4 π}{9} \cdot \frac{180}{π} = 80 °$