Download Find the positive and negative coterminal angle

Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
Find the positive and negative coterminal angle.
1.)
  150 2.)
 
pos: _____
neg: _____
2
3
3.)
pos: _____
neg: _____
  50
pos: _____
neg: _____
Convert to Decimal Degree:
4.) 12345'17" = _________
5.) 10135'10" = ___________
Convert to DMS:
6.) 23.4576 = __________
7.) 103.6754 = ___________
Change from degrees to radians:
8.) 105 = _______
9.) 135 = ________
10.) 50 = ________
Change from radians to degrees:
11.)
3
= _______
4
12.)
7
= _________
6
13.)
11
= ________
4
Find the length of the arc given:
14.)  

4
and r = 16 inches
15.)   110 and r = 3 meters
Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
Find the values of the six trig functions:
16.) sin  _____
csc  _____
cos  _____
sec  _____
tan  _____
cot  _____
7
18.)
x
4
21

16
X = ________
19.)
 = _________
20.)

14
18
5
x
24
X = ________
12
5
Set up a trig equation, then solve for the indicated value.
17.)

13
 = __________
Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
Use your calculator to find the indicated values.
21.) sin 57 = ______
22.) cos 12340’ = ______ 23.) cot 100 = ______
24.) csc 214.73 = _______
25.) sec  = -1.46;  = _________
26.) sin  = .9376;  = _________
27.) csc  = .4819;  = _________
Given sin  = 
5
and  is in quadrant III, find:
13
28.) sin  _____
csc  _____
cos  _____
sec  _____
tan  _____
cot  _____
29.) A man standing 12 ft from the base of a tree has an angle of
elevation to the top of the tree of 33. Find the height of the tree.
30.) A 96-foot tree casts a shadow that is 120 feet long. What is the
angle of elevation of the sun?
31.) From the top of a 200 foot lighthouse, the angle of depression to a
ship in the ocean is 23. How far is the ship from the base of the
lighthouse?
Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
Find the reference angle, and then determine the value of the function.
32.) sin 210
Reference Angle
____________
Value
____
33.) cos 300
____________
____
34.) tan 150
____________
____
35.) sec 225
____________
____
36.) csc 315
____________
____
In which quadrant do the following conditions hold true?
37.) sin  > 0 and cos  < 0 ______ 38.) cos  > 0 and tan  < 0 ______
Identify the amplitude, period, phase shift and vertical shift for each of
the following.
39.) y = 2 cos (4 - )
40.) y = 5 
1
sin 
2
1

41.) y = 1 - sin (   )
2
2
Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
Algebra 3 / Trigonometry
Midterm Review Packet
3
42.) y = -3 cos (3x +
)
2
Name: __________________
Date: ___________ Pd: ___
Amp: __________
Period: __________
Phase Shift: ________
Vertical Shift: _________
Graph the following:
4
3
43.) y = cos ( + )
2
1
- 2
- 3
2
-
-
2

-1

3
2
2
5
2
2
4
7
2
3
-2
-3
-4
4
1

44.) y = 2 sin ( x  )
2
2
3
2
1
- 2
- 3
2
-
-
2

-1

3
2
2
2
5
2
3
7
2
4
-2
-3
4
-4
45.) y = sec (x - )
3
2
1
- 2
- 3
2
-
-
2

-1

3
2
2
5
2
2
4
7
2
3
-2
-3
-4
4
46.) y = 2 csc x
3
2
1
- 2
- 3
2
-
-
2

-1
-2
-3
-4
2

3
2
2
5
2
3
7
2
4
Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
4
47.) y = tan x
3
2
1
- 2
- 3
2
-
-
2

-1

3
2
2
2
5
2
3
7
2
4
-2
-3
-4
4
3
48.) y = cot x
2
1
- 2
- 3
2
-
-
2

-1
2

3
2
2
5
2
3
-2
-3
-4
Find the values using the unit circle:
49.) arcsin ( 
3
) = ________
2
51.) arccos (
2
) = _________
2
50.) sin 1 (1) = ___________
52.) tan 1 ( 3) = ___________
Find the value of the composition function:
53.) sin(arccos
3
) = ________
2
1
54.) tan(arcsin(  )) = ________
2
Simplify using the trig identities:
55.)
tan 
= ________
sin 
56.)
cos2 x  sin2 x
= _________
2
7
2
4
Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
Find the solutions to the given equations over the interval [0, 2 ).
57.) 2 cos x + 1 = 0
58.) 2 sin2 x = 1
59.) 3tan3 x  tan x  0
Use the Law of Sines or the Law of Cosines to solve:
A
60.)
x = __________
80°
12
70°
B
C
x
A
61.)
 = __________
60°
9

B
C
15
62.)
x = __________
A
x
7
63°
B
23
C
Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
A
63.)
 = __________
14
8

B
C
10
64.) From point A on the ground, the angle of elevation to the top of a
tall building is 24. From point B, which is 600 ft closer to the building,
the angle of elevation is measured to be 30. Find the height of the
building.
Building
24°
A
30°
B
Ground
Find the area of the following triangles:
A
65.)
A
66.)
34°
B
B
C
5
Area = _________
14
6
8
Area = __________
C
A
68.)
5
B
17
Area = ___________
A
67.)
12
7
7
C
B
35°
8
Area = ____________
C
Algebra 3 / Trigonometry
Midterm Review Packet
Name: __________________
Date: ___________ Pd: ___
Use a sum or difference formula to find the exact value of the
following:
69.) tan 285
70.) sin 345
71.) cos 195
72.) cos(   ) if cos  
7
,
25
73. sin(   ) if cos   
3
,
5
3
5
3
<  < 2 and sin    ,  <  <
2
13
2


8
<  <  and cos  
, 0<  <
17
2
2