Download Trig. review sheet 1.1-1.4 (student generated

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Trigonometry
Review 1.1-1.4
Find the reference angle for the following angles.
1.  = 300
2.  = 2.3
 - 2.3
60
4.  = 2π
3
3.  = -135
45

3
Solve the following problems.
5. Let (-3,4) be a point on the terminal side of . Find sin , cos , and tan .
r=5
sin  =
cos  =
4
5
-3
5
tan  =
-4
3
6. Determine the exact value of the six trig. functions of  if the terminal side of  passes through the
point (4,3).
r=5
sin  =
csc  =
3
5
5
3
cos  =
sec  =
4
5
5
4
tan  =
cot  =
3
4
4
3
7. Find the exact values of the six trigonometric functions of  given the fact that sin  = 3/5 and  lies
in quadrant II.
x = -4, y = 3, r = 5
sin  =
csc  =
3
5
5
3
cos  =
sec  =
-4
5
-5
4
tan  =
cot  =
-3
4
-4
3
Find two solutions to the following equations given 0 <  < 360.
8.
9.
1
-1
sin  =
sin  =
2
2
30 & 150
10.
23
csc  =
3
210 & 330
60 & 120
Find two solutions to the following equations given 0 <  < 2π.
11. cot  = -1
12. tan  = 1
 & 5
4
4
3 & 7
4
4
Determine two coterminal angles (one positive and one negative) for the following angles.
Positive coterminal angle
Negative coterminal angle
13.  = 35
-325
395
14.  = 3
6
-3
2
5
2
Determine the positive complement and supplement of the following angles.
Complement
15.  = 42
48
16.  = 
4
Supplement
138
3
4

4
Convert the following angles from radians to degrees without the use of a calculator.
17.  = 2
18.  = 5
19.  =4
1440
6
11
7
60
11
Convert the following angles from degrees to radians without the use of a calculator.
20.  = 50
21.  = 320
22.  = 400
16
9
5
18
Convert the following angles to Degrees, Minutes, Seconds.
23.  = 389.501
24.  = 221.689
25.  = -98.690
38930’4”
22141’20”
-9841’24”
720
7
20
9
26. 6.59
37734’45”
Convert the following angles to decimal degrees.
27.  = 6242’24”
28.  = -1010”
62.707
-10.003
Convert the following angles to radians with the aid of a calculator.
29.  = 200
30.  = -42
3.491
-.733
Convert the following angles to degrees with the aid of a calculator.
31.  = 5
32.  = -4.2
286.479
-240.642
Find the third side of the following triangle.
33.
13
12
5
Find the values of the six trigonometric functions of  given the following information. Be sure to
reduce all answers.
34.
10

sin  =
3
5
6
8
cos  =
4
5
tan  =
csc  =
3
4
sec  =
5
3
cot  =
5
4
4
3
35.
6
5

11
sin  =
5
6
cos  =
11
6
tan  =
csc  =
sec  =
6
5
511
11
cot  =
11
5
611
11
Sketch a right triangle corresponding to the trigonometric function of the acute angle . Then
determine the other five trigonometric functions of .
36. sin  = 3
4
x = 7, y = 3, r = 4
cos  =
7
4
tan  =
37
7
37. cos  = 1
2
sin  =
3
2
csc  =
sec  =
cot  =
47
7
4
3
7
3
x = 1, y = 3, r = 2
tan  =
csc  =
sec  =
23
3
3
cot  =
2
3
3
38. cot  = 5
x = 5, y = 1, r = 26
sin  =
26
26
cos  =
526
26
tan  =
csc  =
1
5
26
sec  =
26
5
Solve the following real life situations using your knowledge of right triangle trigonometry.
39. A steel cable zip-line is being constructed for a competition on a reality TV show. One end of the
zip-line is attached to a platform on top of a 160 foot pole. The other end of the zip-line is attached to
the top of a 6 foot stake. The angle of elevation to the platform is 23.
160
x
154
23
y
b. How far is the stake from the pole?
6
a. How long is the zip line?
394.13 ft.
362.80 ft.
40. You are standing 45 meters from the base of the Empire State Building. You estimate that the angle
of elevation to the top of the 86th floor to be 82. If the total height of the building is another 123
meters above the 86th floor, what is the approximate height of the building?
123
320.19 m
x
82
45
82
45
Solve the following for x (exact value if possible).
41.
30
45
42.
22
x = 152
x
x = 50.71
18
x
Determine the ordered pair that is associated with the following angles and then calculate the given
trigonometric function.
Angle
Ordered Pair
Trig. Function
43.  = 120
tan

=
-1
44.  = 5
4
45.  = 720
46.  = 
4
3
2, 2
-2 -2
2, 2
-3
sec  =
cot  =
1, 0
2 2
2, 2
cos =
-2
undefined
2
2
47.  = 5
6
State the quadrant in which  lies.
48. sin  > 0 and tan  < 0.
-3 1
2, 2
Quadrant II
sin  =
1
2