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NAME
DATE
4-1
PERIOD
Practice
Right Triangle Trigonometry
Find the exact values of the six trigonometric functions of θ.
√
55
8
3
, cos θ = − ,
sin θ = −
θ
8
3
2.
24
,
sin θ = −
7
θ
8
3 √
55
8
,
tan θ = − , csc θ = −
55
3
√
8 √
55
55
sec θ = − , cot θ = −
55
3
25
7
cos θ = −
,
25
25
24
tan θ = −
, csc θ = −
,
7
24
25
7
sec θ = −
, cot θ = −
7
24
24
Find the value of x. Round to the nearest tenth, if necessary.
3.
35.3
4.
9.4
26°
x
19.2
56°
x
63.1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. On a college campus, the library is 80 yards due east of the dormitory and the recreation
center is due north of the library. The college is constructing a sidewalk from the
dormitory to the recreation center. The sidewalk will be at a 56° angle with the current
sidewalk between the dormitory and the library. To the nearest yard, how long will the new
sidewalk be? 143 yd
6. If cot A = 8, find the exact values of the remaining trigonometric functions for
the acute angle A.
√
√
65
8 √
65
65
1
sin A = − , cos A = − , tan A = −
, sec A = − , csc A = √
65
65
65
8
8
Find the measure of angle θ. Round to the nearest degree, if necessary.
7.
2
4
8.
θ
θ
3
7
42°
55°
Solve each triangle. Round side measures to the nearest tenth and angle
measures to the nearest degree.
9. "
22°
$
14
a ≈ 5.2,
b ≈ 13.0,
B = 68°
10.
$
7
"
#
2
c
c ≈ 7.3,
A ≈ 16°,
B ≈ 74°
#
11. SWIMMING The swimming pool at Perris Hill Plunge is 50 feet long and 25 feet wide.
If the bottom of the pool is slanted so that the water depth is 3 feet at the shallow end
and 15 feet at the deep end, what is the angle of elevation at the bottom of the pool?
about 13.5°
Chapter 4
7
Glencoe Precalculus
Lesson 4-1
1.
NAME
DATE
4-1
PERIOD
Word Problem Practice
Right Triangle Trigonometry
1. MONUMENTS The Leaning Tower of
Pisa in Italy is about 55.9 meters tall
and is leaning so it is only about
55 meters above the ground. At what
angle is the tower leaning?
5. OBSERVATION A person standing
100 feet from the bottom of a cliff notices
a tower on top of the cliff. The angle of
elevation to the top of the cliff is 30°, and
the angle of elevation to the top of the
tower is 58°. How tall is the tower?
about 10.3°
about 102.3 ft
2. SUBMARINES A submarine that is
250 meters below the surface of the ocean
begins to ascend at an angle of 22° from
vertical. How far will the submarine
travel before it breaks the surface of the
water?
58°
about 269.6 m
30°
100 ft
3. PHYSICS Suppose you are traveling in a
car when a beam of light passes from the
air to the windshield. The measure of the
angle of incidence θi is 55°, and the
measure of the angle of refraction
sin θ
θr is 35.25°. Use Snell’s Law, −i = n,
6. GEOMETRY The apothem of a regular
polygon is the measure of the line segment
from the center of the polygon to the
midpoint of one of its sides. A circle is
circumscribed about a regular hexagon
with an apothem of 4.8 centimeters.
sin θr
to find the index of refraction n of the
windshield to the nearest thousandth.
4.8 cm
4. CONSTRUCTION A 30-foot ladder
leaning against the side of a house makes
a 70.1° angle with the ground.
a. Find the radius of the circumscribed
circle. about 5.5 cm
b. What is the length of a side of the
hexagon? about 5.5 cm
c. What is the perimeter of the
hexagon? about 33 cm
30 ft
7. SKATEBOARD Suppose you want to
construct a ramp for skateboarding with a
19° incline and a height of 4 feet.
70.1°
a. How far up the side of the house does
the ladder reach?
a. Draw a diagram to represent
the situation.
about 28.2 ft
b. What is the horizontal distance
between the bottom of the ladder
and the house?
4 ft
19°
about 10.2 ft
b. Determine the length of the ramp.
about 12.3 ft
Chapter 4
8
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
about 1.419
NAME
DATE
4-2
PERIOD
Practice
Degrees and Radians
Write each decimal degree measure in DMS form and each DMS measure in
decimal degree form to the nearest thousandth.
1. 28.955°
2. -57.3278
28° 57' 18"
3. 32° 28' 10"
32.469°
-57° 19' 40.08"
4. -73° 14' 35"
-73.243°
Write each degree measure in radians as a multiple of π and each radian
measure in degrees.
5π
−
5. 25°
3π
7. −
4
13π
−
6. 130°
36
18
5π
8. −
3
135°
300°
Identify all angles that are coterminal with the given angle. Then find and draw
one positive and one negative angle coterminal with the given angle.
9. 43°
7π
10. − −
43° + 360n°
y
4
y
y
43°
x
403°
− + 2nπ
− 7π
43°
-317°
4
y
π
4
x
- 7π
4
- 15π
4
x
x
−, − 15π
Sample answers: π
−
Sample answers: 403°, −317°
4
4
Find the length of the intercepted arc with the given central angle measure
in a circle of the given radius. Round to the nearest tenth.
11. 30°, r = 8 yd 4.2 yd
−, r = 10 in. 36.7 in.
12. 7π
6
Find the rotation in revolutions per minute given the angular speed and
the radius given the linear speed and the rate of rotation.
4
π rad/s 24 rev/min
13. ω = −
5
14.
V
= 32 m/s, 100 rev/min 3.06 m
15. On a game show, a contestant spins a wheel. The angular speed of the wheel
π
was ω = − radians per second. If the wheel maintained this rate, what would be
3
the rotation in revolutions per minute? 10 rev/min
Find the area of each sector.
π
16. θ = −
, r = 14 in. 51.3 in2
6
14 in.
Chapter 4
7π
17. θ = −
, r = 4 m 44.0 m2
4
π
6
7π
4
12
4m
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
- 7π
4
NAME
DATE
4-3
PERIOD
Practice
Trigonometric Functions on the Unit Circle
The given point lies on the terminal side of an angle θ in standard position.
Find the values of the six trigonometric functions of θ.
1. (−1, 5)
2. (7, 0)
√
26
5 √
26
sin θ = − , cos θ = - − ,
26
26
√
26
tan θ = −5, csc θ = − ,
3. (−3, −4)
sin θ = - − , cos θ = - − ,
5
1
sec θ = - √
26 , cot θ = − −
5
4. (1, −2)
tan θ = − , csc θ = - − ,
3
√
5
5
4
3
3
4
sec θ = - − , cot θ = −
sec θ = 1, cot θ = undefined
5. (−3, 1)
2 √
5
5
5
4
tan θ = 0, csc θ = undefined,
5
3
4
sin θ = 0, cos θ = 1,
6. (2, −4)
√
10
3 √
10
10
1
10
2 √
5
√5
sin θ = - − , cos θ = − ,
sin θ = − , cos θ = - − ,
sin θ = - − , cos θ = − ,
tan θ = -2, csc θ = - − ,
tan θ = - − , csc θ = √
10 ,
tan θ = -2, csc θ = - − ,
sec θ = √
5 , cot θ = - −
sec θ = - − , cot θ = -3
, cot θ = - −
sec θ = √5
5
√5
5
2
1
2
3
√
10
3
5
5
√5
2
1
2
Sketch each angle. Then find its reference angle.
y
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
θ = 330°
θ = 30°
π
−
4
4
0
θ = π
6
6
θ = π
π
−
π
12. − −
45°
y
3
3
x
0
y
θ = 135°
θ = 45°
4
x
x
0
θ = π
x
0
6
4
y
θ = 7π
y
θ = 7π
θ = - 3π
4
11. 135°
4
6
x
x
0
π
−
7π
9. −
0
θ =-π
3
4
θ = π
3
Find the exact value of each expression. If undefined, write undefined.
13. csc 90°
1
14. tan 270°
3π
16. cos −
0
π
17. sec − −
2
undefined
√
2
( 4)
15. sin (−90°)
5π
18. cot −
6
−1
- √3
19. PENDULUMS The angle made by the swing of a pendulum and its vertical resting
position can be modeled by θ = 3 cos πt, where t is time measured in seconds and θ is
measured in radians. What is the angle made by the pendulum after 6 seconds? 3 rad
Chapter 4
17
Glencoe Precalculus
Lesson 4-3
4
y
7π
10. −
π
−
3π
8. − −
30°
7. 330°