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1.
An observer is 120 feet from the base of a television tower which is 150 feet tall.
Find, to the nearest degree, the angle of elevation of the top of the tower from the
point where the observer is standing.
2.
From the top of a vertical cliff which is 40 meters high, the angle of depression of an
object that is level with the base of the cliff is 34º. How far is the object from the
base of the cliff, to the nearest meter?
3.
An airplane is flying at an altitude of 1000 meters. From the plane, the angle of
depression to the base of a tree on the ground is measured as 15°. What is the
distance from the plane to the base of the tree, rounded to the nearest tenth of a
meter?
4.
From a 200 feet high cliff a boat is
noticed floundering at sea! The boat
is approximately 300 yards from
the base of the cliff. What is the
angle of depression, to the nearest
degree, of the line of sight to the
boat?
Homework #2
Name___________________________________
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State the quadrant in which the terminal side of each angle lies.
1) -170°
2) -240°
3) 285°
4) -105°
Find a positive and a negative coterminal angle for each given angle.
5) -605°
6) 245°
7) -290°
8) 534°
Find the reference angle.
9)
10)
y
y
-395°
x
x
385°
11) 520°
12) 405°
13) 120°
14) 280°
Find the exact value of each trigonometric function.
15) cos q
16) sin q
y
y
x
x
-120°
17) cot q
-495°
18) csc q
y
x
y
-30°
x
-600°
Worksheet by Kuta Software LLC
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Homework #3
ANGLES IN STANDARD POSITION WORKSHEET
In which quadrant does the terminal side of the each angle lie?
1. 150o
2. -60o
3. -240o
4. 540o
Sketch the angles in standard position.
5.
100
6.
45
7.
720
Name four coterminal angles for each angle given.
Be sure to include at least one negative angle measure for each.
8.
135
9.
30
Name the reference angle for each of the given angles.
10.
330
11.
225
12.
400
13.
240
14.
30°
15.
260°
Determine the six trig functions exact value given a point on the terminal side of an angle in
standard position.
16.
Given the point ( 5, -7 ) on the terminal side of an angle.
17.
Given the point ( -6, -4 ) on the terminal side of an angle, determine the six trig functions.
Evaluate trig values given one value and other information.
18.
Given sin  
3
4
19.
Given tan  
5
3
and cos   0 , evaluate tan  and sec .
and θ is in Quadrant IV, evaluate sin  and sec .
Homework #4
Name___________________________________
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Draw an angle with the given measure in standard position. Then state the reference angle.
1)
5p
4
2) -
9p
4
y
y
x
x
Find a positive and a negative coterminal angle for each given angle.
3) -
7p
3
Convert each degree measure into radians.
4) 120°
Convert each radian measure into degrees.
5)
3p
2
Find the exact value of each trigonometric function.
6) cos q
7) sin q
y
y
x
x
2p
3
3p
4
Find the length of each arc.
8)
9)
p
4
16 yd
13 mi
p
3
Worksheet by Kuta Software LLC
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Trigonometric Functions Maze
Directions: Every angle has a match. Pick three different colors, shade sine angles and measures in one
color, cosine angles and measures in a second color and tangent angles and measures in the third color.
sin
𝜋𝜋
6
1
2
−√3
5𝜋𝜋
3
tan
cos 𝜋𝜋
1
2
−1
sin
𝜋𝜋
4
1
1
2
cos
tan
−
tan
7𝜋𝜋
4
√2
−
2
5𝜋𝜋
6
2𝜋𝜋
3
−1
5𝜋𝜋
sin
4
© 2014 FlamingoMath.com
cos
𝜋𝜋
3
1
2
tan
0
cos
3𝜋𝜋
4
tan 𝜋𝜋
−
√2
2
√2
2
tan
sin
𝜋𝜋
4
𝜋𝜋
3
1
𝜋𝜋
6
√3
3
𝜋𝜋
6
sin 𝜋𝜋
−
cos 2𝜋𝜋
0
Undef.
sin
1
2
tan
𝜋𝜋
2
√3
2
√3
5𝜋𝜋
3
cos
11𝜋𝜋
6
sin
√3
2
tan
sin
√3
2
cos
4𝜋𝜋
3
√3
cos
𝜋𝜋
3
√3
2
𝜋𝜋
2
1
2𝜋𝜋
3
sin
1
cos
4𝜋𝜋
3
cos
7𝜋𝜋
6
1
2
3𝜋𝜋
2
0
tan
−
5𝜋𝜋
4
1
2
Jean Adams
Homework #5
Name___________________________________
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Assignment
Solve each triangle. Round your answers to the nearest tenth.
1) m A = 34°, m B = 37°, a = 13 km
2) m B = 148°, m C = 18°, a = 11 km
3)
4)
A
28 cm
B
27 cm
A
21 m
84°
24 m
C
C
25 cm
B
5) m C = 41°, b = 34 yd, c = 27 yd
6) m C = 41°, b = 32 mi, c = 31 mi
Find each measurement indicated. Round your answers to the nearest tenth.
7) m B = 104°, a = 23 yd, b = 15 yd
Find m C
Worksheet by Kuta Software LLC
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Name___________________________________
HOMEWORK #7
Graph two full periods of each function. Label the scale on both axes.


1. y  sin  x  

3
Amplitude:
Period:
Phase Shift:
Vertical Displacement:
Reflection?
2. f ( x)  2  tan x
Amplitude:
Period:
Phase Shift:
Vertical Displacement:
Reflection?
3. y  cos  2 x   
Amplitude:
Period:
Phase Shift:
Vertical Displacement:
Reflection?
4. y  tan  4 x     1
Amplitude:
Period:
Phase Shift:
Vertical Displacement:
Reflection?
5. f ( x)  1  cos x
Amplitude:
Period:
Phase Shift:
Vertical Displacement:
Reflection?
6. y  1 2 sin  2 x  3 
Amplitude:
Period:
Phase Shift:
Vertical Displacement:
Reflection?
Write an equation of the graph described.
7. The graph of
y  tan x translated down 4 units and left 1 unit.
8. The reflection of the graph of
9. The graph of
y  cos x with a period of 4π.
y  sin x with an amplitude of 4 that is translated right 3 units.
10. The reciprocal of
y  sin x that is translated left 5 units and up 4 units.
Homework #9
Using a calculator, solve each equation to the nearest tenth. Use the given restrictions.
1.
tan   1.4 , for 90    90
3.
sin   0.75 , for 180    270
2.
cos  0.25 , for 0    180
Without using a calculator, solve each equation. Solve for all angles 0    2 .
4.
Solve 3tan   tan   2
5.
Solve 2cos   3  0
6.
Solve 2sin   1  2  sin 
7.
Solve sin 2   2sin   3 , for
8.
Solve cos2   2cos   3 , for
9.
Solve 2cos2   sin   1, for
10.
Solve sin 2   sin   0 , for
Homework #10 Trig Identities Puzzle