PreCalculus
Review 6.1, 6.2
Name: _______________________________
Change each degree measure to radian measure in terms of π.
1.
6°
2. -145°
Change each radian measure to degree measure. Round to the nearest tenth if necessary.
3.
13𝜋
30
4.
4π
Use the Unit Circle to find the following trig values. Give exact answers.
5.
cos 
7. tan
7
3
6. csc
7
4
8.
17
6
cot
−
9𝜋
2
9.
Find the area of a sector if the central angle measures 66o and the radius of the circle is 12.1 yards. Round
to the nearest tenth.
10.
Given a central angle of
to the nearest tenth.
3𝜋
5
radians, find the length of its intercepted arc in a circle of radius 10 cm. Round
Find the angular displacement θ (i.e. radian measure).
11.
11.5 revolutions
12. 6 revolutions
Find the angular velocity ω (in radians per second).
13.
5.5 revolutions in 4 minutes
14.
22.4 revolutions in 15 seconds
15.
A clothes dryer is rotating at 500 revolutions every 50 seconds.
Find the linear velocity in inches per second.
14.
ω = 28 radians per second, r = 2 feet
15. Suppose the second hand on a clock is 3 inches long. Find the linear velocity of the second hand.
Solve.
16. Find the degree measure of the central angle associated with an arc that is 21 cm long in a circle with
a radius of 4 cm.
17.
An arc is 21.4 cm long and is intercepted by a central angle of
3𝜋
8
radians. Find the diameter of the
circle.
18.
A belt runs a pulley that has a diameter of 8 cm. If the pulley rotates at 100 revolutions per minute,
what is its angular velocity in radians per second and its linear velocity in cm per second?
19. Two pulleys, one with radius 2 inches and the other with radius 8 inches, are connected by a belt. If
the 2 inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per
minute of the 8 inch pulley. (Hint: The linear speeds of the pulleys, that is the speed of the belt, are
the same.)
20. To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is
lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per
minute, what is the speed of the current? Express your answer in miles per hour.