Download state the quadrant in which each angle lies given it is in standard

PRE-CALCULUS WORKSHEET 4.1 – 4.4
NAME
CONVERT EACH ANGLE TO RADIANS. EXPRESS YOUR ANSWER AS A MULTIPLE OF .
1.
18°
2.
300°
3.
-225°
6.
-3
CONVERT EACH ANGLE TO DEGREES.
4.

9
5.
7

6
STATE THE QUADRANT IN WHICH EACH ANGLE LIES GIVEN IT IS IN STANDARD POSITION
7.
14

3
8.
780°
9.
-380°
FIND A POSITIVE ANGLE LESS THAN 360° OR 2 THAT IS COTERMINAL WITH THE GIVEN
ANGLE.
10.
415°
11.
17

5
12.
-765°
FIND THE LENGTH OF THE ARC ON A CIRCLE OF RADIUS r INTERECEPTED BY A CENTRAL
ANGLE . EXPRESS ARC LENGTH IN TERMS OF .
13.
r = 12 inches,  = 45°
14.
r = 9 yards,  = 315°
15.
The minute hand of a clock moves from 12 to 2 o’clock, or 1 of a complete revolution. (A) Through
6
how many degrees does it move? (B) Through how many radians does it move?
16.
The minute hand of a clock is 6 inches long and moves from 12 to 4 o’clock. How far does the tip of the
minute hand move? Express your answer in terms of . [Hint: Find the arc length.]
17.
Find the angular velocity in radians per second of the second hand of a clock. Express the answer in
terms of . Show work.
18.
Calculate the angular velocity in radians per minute of a Ferris wheel with a diameter of 208 feet that
takes 25 seconds to rotate once. Express the answer in terms of . Show work.
19.
If you sat on the rim of the Ferris wheel in #18, what would your linear velocity be, to the nearest foot
per minute. Show work.
20.
A flywheel mounted on an engine crankshaft has a radius of 6 inches. If the engine is running at
2800 rpm, what is the linear velocity of a point on the outer edge of the flywheel in feet per second?
Show work.

USE EVEN AND ODD PROPERTIES OF TRIGONOMETRIC FUNCTIONS AND YOUR ANSWER
FROM (A) TO FIND THE ANSWER TO (B).
21.
 
(A) cos  
3
22.
 
(B) cos   
 3
 
(A) tan  
4
 
(B) tan   
 4
USE A CALCULATOR TO FIND THE VALUE OF THE TRIGONOMETRIC FUNCTION TO FOUR
DECIMAL PLACES.
24.
 
cos  
 10 
25.
 
cot  
 12 
23.
sin 0.8
27.
Use the triangle to find each of the six trigonometric functions of .
26.
6
sec 1
5

USE RIGHT TRIANGLE RATIOS TO SOLVE THE FOLLOWING. SHOW WORK.
28.
A building that is 21 meters tall casts a shadow 25 meters long. Find the angle of elevation of the sun to
the nearest degree.
29.
Sighting the top of a building, a surveyor measured the angle of elevation to be 22°. The transit is 300
feet from the building. Find the building’s height, to the nearest foot, if the transit if 5 feet off the
ground.
30.
A plane rises from take-off and flies at an angle of 10° with the horizontal runway. When it has gained
an altitude of 500 feet, find the distance, to the nearest foot, the plane has flown.
31.
If (-4, 3) is a point on the terminal side of angle , find the exact value of each of the six trigonometric
functions of .
LET  BE AN ANGLE IN STANDARD POSITION. NAME THE QUADRANT IN WHICH  LIES.
32.
sin  < 0, cos  < 0
33.
cot  > 0, sec  < 0
FIND THE REFERENCE ANGLE FOR EACH ANGLE.
34.
160°
35.
-250°
36.
7

4
37.

13

3
FIND THE EXACT VALUE OF EACH EXPRESSION. DO NOT USE A CALCULATOR. USE A
REFERENCE ANGLE WHEN NECESSARY.
38.
cos 45°
39.
sin 180°
40.
cot 120°
41.
sec (-30°)
42.
csc (-390°)
43.
tan (765°)
44.
tan

4
45.
cos
5

4
46.
csc 
47.
sin
20

3
48.
2
sec  
3
49.
 7 
cot    
 6 