Download PreCalculus 1. Find an angle that is complementary to: 3

PreCalculus
4.1-4.4
Test Review
1. Find an angle that is complementary to:
a. θ =
3
11
b. θ =
2
7
b. θ =
3
8
2. Find an angle that is supplementary to:
a. θ =

10
3. Determine one coterminal angle Ө for -
4. Determine one coterminal angle Ө for
7
so that 0 ≤ Ө < 2π
6
9
so that 0 ≤ Ө < 2π
2
5. Convert to radian measure: a) 36°
6. Convert to degrees: a)
5
6
b) –120°
b) 
11
30
7. Find the arc length, s, of a circle if its central angle is 4 rad and the radius is 5 units.
8. Find the radius of a circle with a central angle of 2 rad and arc of 18 units.
9. Find the central angle of a circle if the radius is 8 units and the arc is 12 units.
10. Find the arc length, s, of a circle if its central angle is 100° and the radius is 18 units.
11. Find the radius of a circle with a central angle of 72° and arc of 6 units.
12. Evaluate each of the following:
a. sin
5
4
b. cos
2
3
17
 
c. tan   d. sin
6
 6
7
 5 
e. cos 
 f. tan
2
 4 
13. Solve for x.
27
24
x
14. The point given is on the terminal side of an angle in standard position. Determine all six
trigonometric values of the angle: (-5, 3)
15. The point given is on the terminal side of an angle in standard position. Determine all six
trigonometric values of the angle: (-2, -1)
16. tan  
7
and cosθ < 0. Find sinθ and secθ
3
17. cos   
1
and sinθ < 0. Find tanθ and cscθ
4
18. A cable is attached to the top of a 120 foot high pole and is then attached
to the ground forming a 40 angle with the ground. How long is the cable?
19. A 12-foot extension ladder leans against the side of a building. Find the distance, h,
up the side of the building if the angle of elevation of the ladder is 62º.
20. The length of a shadow of a tree is 48 feet when the angle of elevation of the sun is
38º. Approximate the height of the tree.
Solutions
5
1. a.
22
2.
a.
3.
5
6
4.

2
5. a.
9
10

5
3
14
b.
5
8
b. 
6. a. 150°
12. a. 
2
2
b. 
a. x 
24
sin 27
14.
sin  
3 34
34
1
2
c. 
cos   
3
3
cos   
2 5
5
7 58
58
sec  
58
3
17. tan  15
csc  
120
 186.7 ft
sin 40
19. h  12 sin 62  10.6 ft
20. t  48 tan 38  37.5 ft
d.
5 34
34
5
5
15. sin   
10. s  10  31.416
9.   1.5rad
8. r = 9
13.
16. sin  
2
3
b. -66°
7. s = 20
18. c 
b.
15
4
1
2
e. 
tan  
tan  
1
2
3
5
2
2
11.
r
15

 4.775
f. undefined
csc 
csc    5
34
3
sec  
sec  
5
2
34
5
cot   
cot   2
5
3