Download 23. cos "3 24. tan "4

Geometry Trigonometry Review
Angles and Radians A
Name
Date - - - - - - ­
Period - - -
Match the angle measure with the angle.
2.
1. - 320 0
A.
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67T
3. 4
5
B.
y
C.
y
y
P"
x
x
x
Draw an angle with the given measure in standard position.
87T
4. 100 0
6.
9
127T
7.
5
Find one positive angle and one negative angle coterminal with the
given angle.
10.
1517"
-2
11.
l61T
5
Rewrite each degree measure in radians and each radian measure
in degrees.
12. 135°
16 ­
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. 12
13. 40°
14. 260°
17.
18.
15. 215°
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71'
3
19.
"6
Find the arc length of a sector with the given radius r and central
angle 6.
20. r = 4 in., 8
= ;
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21.r=5m8=,
12
22. r
=
12 cm,
e = 210°
Evaluate the trigonometric function using a calculator if necessary.
If possible, give an exact answer.
23. cos
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"3
7T
24. tan "4
•
27T
25 . sm5
27. Pendulum The pendulum of a grandfather clock is 4 feet long and
swings back and forth creating a 60° angle. Find the length of the arc of
the pendulum, after one swing.
7T
26 . cos­8
Geometry Trigonometry Review
Angles and Radians B
Name - - - - - - - - ­
Date - - - - - - - - ­
Period - - ­
Draw an angle with the given measure in standard position.
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1. 215°
3.
Find one positive angle and
given angle.
on~
12
57T
4.
6
negative angle coterminal with the
6. 540°
7.
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207T
3
8. -5­
Rewrite each degree measure in radians and each radian measure
in degrees.
10. -340°
9. 210°
13.
137T
4
14.
87T
3
11. 165°
12. 100°
15.
16.
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12
Find the arc length of a sector with the given radius r and central
angle O.
17. r = 12 ft, () =
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2
18. r
.
= 2 m.,
()
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=4
19. r
= 20 m,
()
= 180°
Evaluate the trigonometric function using a calculator if necessary.
If possible, give an exact answer.
7T
3
20. sm-
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24. sec6
28.
7T
21. tan -
8
7T
25. csc-
4
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22. sm-
2
37T
27. cot­
8
Fire Truck Ladder For the ladder on a fire truck to
operate properly, the base of the ladder must be almost
level. The diagram at the right shows part of a leveling
device that is used to determine whether the level of the
ladder's base is within the allowable range. Find the
length of the arc that describes the allowable range.
29.
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26. cos 15
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7
23. cos­
Allowable {
range
Snowboarding During a competition, a snowboarder perlonns a trick
involving three revolutions. Find the measure of the angle generated as the
snowboarder perlorms the trick. Give the answer in both degrees and
radians.
8
Geometry Trigonometry Review
Angles and Radians C
Name
--------Date
--------Period - - -
Draw an angle with the given measure in standard position.
77T
1.
157T
15
2.
-4
4. 500°
Find one positive angle and one negative angle coterminal with the
given angle.
47T
5. 105°
8.
7. 3
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4
Rewrite each degree measure in radians and each radian measure
in degrees.
9. 315°
13.
10. -75°
57T
(5
14.
37T
4
27T
15.
9
16. 3
Find the arc length of a sector with the given radius r and central
angle 6.
17. r
=
13 cm, f3 =
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"3
19. r = 8 m, f3
18. r = 10.5 in., f3 = 150°
= 210°
Evaluate the trigonometric function using a calculator if necessary.
If possible, give an exact answer.
7T
20. cot 3
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21. tan 3
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22. csc -
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23. cos­
5
77T
24. sin 15
37T
25. sec8
7T
26. cot 6
27. csc ­
28. Bicycles A bicycle's gear ratio is the
number of times the freewheel turns for every
one tum of the chainwheel. The table shows
the number of teeth in the freewheel and
chainwheel for the fust 5 gears on an 18-speed
bicycle. In first gear, if the chainwheel
completes 2 rotations, through what angle
does the freewheel tum? Give your answer in
both degrees and radians.
8
Gear
Number
Number of teeth
in freewheel
Number of teeth
in chainwheel
1
32
24
2
26
24
3
22
24
4
32
40
5
19
24
29. Earth Assuming that Earth is a sphere of diameter 8000 miles,
what is the distance between city A and city B in the figure shown
if the central angle is 60°?
"-.­
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