1) Convert the following degree measures to radians. Leave your answer in terms of \(\pi\).
a) \(30^{\circ}\)
b) \(45^{\circ}\)
c) \(90^{\circ}\)
d) \(135^{\circ}\)
e) \(270^{\circ}\)
f) \(100^{\circ}\)
g) \(195^{\circ}\)
2) Convert the following radian measures to degrees.
a) \(\Large\frac{3\pi}{4}\)
b) \(\Large\frac{5\pi}{6}\)
c) \(\Large\frac{7\pi}{12}\)
d) \(\Large\frac{5\pi}{8}\)
e) \(\Large\frac{2\pi}{3}\)
f) \(1.5\)
g) \(2.2\)
3) What is the arc length of a circle with the following measurements? Leave your answer in terms of \(\pi\).
a) radius length = \(14\) cm and radian measure \(\theta\) of \(\Large\frac{\pi}{4}\).
b) radius length = \(4.3\) ft and radian measure of \(\Large\frac{7\pi}{6}\).
c) radius length = \(23.4\) mm and radian measure of \(\Large\frac{3\pi}{8}\).
d) radius length = \(5\) m and radian measure of \(\Large\frac{\pi}{3}\).
4) What is the arc length of a circle with the following measurements?
a) radius length = \(7\) in and radian measure of \(8\)
b) radius length = \(2.2\) km and radian measure of \(1.9\)
5) What is the radius of a circle with an arc length of \(24\) in. and a central angle measure of \(\Large\frac{4\pi}{3}\)? Leave your answer in terms of \(\pi\).
6) What is the arc measure in radians of a circle with a radius of \(13.3\) cm and an arc length of \(4.1\) cm?
Solution Bank
a) \(30^{\circ}\)
b) \(45^{\circ}\)
c) \(90^{\circ}\)
d) \(135^{\circ}\)
e) \(270^{\circ}\)
f) \(100^{\circ}\)
g) \(195^{\circ}\)
2) Convert the following radian measures to degrees.
a) \(\Large\frac{3\pi}{4}\)
b) \(\Large\frac{5\pi}{6}\)
c) \(\Large\frac{7\pi}{12}\)
d) \(\Large\frac{5\pi}{8}\)
e) \(\Large\frac{2\pi}{3}\)
f) \(1.5\)
g) \(2.2\)
3) What is the arc length of a circle with the following measurements? Leave your answer in terms of \(\pi\).
a) radius length = \(14\) cm and radian measure \(\theta\) of \(\Large\frac{\pi}{4}\).
b) radius length = \(4.3\) ft and radian measure of \(\Large\frac{7\pi}{6}\).
c) radius length = \(23.4\) mm and radian measure of \(\Large\frac{3\pi}{8}\).
d) radius length = \(5\) m and radian measure of \(\Large\frac{\pi}{3}\).
4) What is the arc length of a circle with the following measurements?
a) radius length = \(7\) in and radian measure of \(8\)
b) radius length = \(2.2\) km and radian measure of \(1.9\)
5) What is the radius of a circle with an arc length of \(24\) in. and a central angle measure of \(\Large\frac{4\pi}{3}\)? Leave your answer in terms of \(\pi\).
6) What is the arc measure in radians of a circle with a radius of \(13.3\) cm and an arc length of \(4.1\) cm?
Solution Bank