June 28, 2012
Worksheet 6
Name: ___________________
3.3 Circular Functions
1. Use a filled in unit circle to find the sine, cosine, and tangent of
2. Use the unit circle to find all values of t between 0 and
.
3. Find
/3.
for which
if corresponds to the point (0.8290, 0.5592) on the unit circle.
4. Evaluate
( )
5. Determine which of the statements are possible for some real number :
a.
6. Describe how
b.
varies as increases from
c.
to /2.
3.4 Arc Length and Area of a Sector
7. Give the are length of the arc cut off by a central angle of 3.1 radians in a circle
of radius 5.4 inches.
8. The minute hand of a clock is 2.4 centimeters long. To two significant digits,
how far does the tip of the minute hand move in 15 minutes?
9. A person standing on the earth notices that a 747 jumbo jet flying overhead
subtends and angle of 0.56 . If the length of the jet is 235 feet, find the altitude
to the nearest thousand feet.
10. Find the area of a sector formed by a central angle of 1.6 radians in a circle of
radius 3.5 meters.
11. If the sector formed by a central angle of 30 has an area of
square
centimeters, find the radius of the circle.
12. A lawn sprinkler located at the corner of a yard is set to rotate through 60
and project water out 25.5 feet. What area of lawn is watered by the sprinkler?
3.5 Velocities
13. A point on a circle travels 8 centimeters in 5 seconds. Find the linear velocity
of the point.
14. A point P on a circle rotates through
angular velocity of P.
radians in 4 seconds. Give the
15. A bicycle wheel with a radius of 15.0 inches turns with an angular velocity of 5
radians per second. Find the distance traveled by a point on the bicycle tire in 1
minute.
16. A phonograph record is turning at 33 revolutions per minute (rpm). If the
distance from the center of the record to a point on the edge of the record is 4
inches, find the angular velocity of the point (in feet per minute).