Angles and Their Measure
1. Perform the indicated conversion:
SOLUTION
(a) Convert \(70^\circ\) and \(160^\circ \) to radians. Express your
answer as a multiple of \(\pi\).
(b) Convert \(\frac{\pi}{4} \) and \( \frac{2\pi}{9}\) radidans
to degrees.
2. A sector is formed on a circle of radius \( r \) by a central
angle \( \theta\). Let \(s\) be the arc length and \(A\) be the area of
the sector. Find the missing quantity with correct units.
SOLUTION
(a) \( r=4\) meters, \(\theta=45^\circ, s= ? \)
(b) \( r=5 \) miles, \(s=3\) miles, \(\theta= ? \)
(c) \( \theta=\frac{\pi}{4}\) radians, \(r=20\) feet, \(A= ? \)
(d) \(\theta=\frac{1}{4}\) radians, \(A=6\) square inches, \(r=?\)
3. A pendulum swings through an angle of \(20^\circ\) each second. If
the pendulum is 40 inches long, how far does its tip move each second?
SOLUTION4. A water
sprinkler sprays water over distance of 20 ft while
rotating through an angle of \(135^\circ\). What area of lawn receives water? SOLUTION
