Precalculus
Unit 4 - Trigonometry
Name:
Date:
2-6-14 and 2-7-14
Homework: Unit Circle and Reference Angles #3
In which quadrant does the terminal side lie? Determine the reference angle, β.
Sketch the angle in standard position to support your response.
1.
124°
2.
78°
3.
–36°
4.
580°
5.
–450°
6.
7π
3
7.
17π
6
8.
−
8π
3
9.
9π
2
10.
–2 π
11.
7π
9
12.
−8π
10
Write the ordered pair for each angle measure on the unit circle. Give exact value(s).
Use a coterminal angle and/or reference angle if the given angle is not between 0 and 2π.
Sketch the angle in standard position to support your response.
13.
 15π 


 4 
14.
 23π 


 6 
15.
 −10π 


 6 
16.
 −15π 


 2 
17.
 47π 


 6 
18.
 −13π 


 3 
Evaluate each trigonometric function without a calculator. Give exact simplified values.
Use a coterminal angle and/or reference angle if the given angle is not between 0 and 2π.
Sketch the angle in standard position to support your response.
9π 

 4 
20.
sin 
−7π 

 6 
23.
tan 
−4π 

 3 
26.
tan 
7π 

 3 
29.
sin 
−7π 

 6 
32.
sec 
19.
sin 
22.
cos 
25.
sec 
28.
cot 
31.
csc 
5π 

 2 
21.
cos 
−7π 

 3 
13π 

 6 
24.
cot 
19π 

 6 
27.
csc ( −5π )
201π 

 4 
30.
cos 
85π 

 4 
33.
tan 
8π 

 3 
35π 

 6 
41π 

 3 
The point given is on the terminal side of an angle θ in standard position.
Determine the exact values of the six trigonometric function of the angle without a calculator.
Simplify and rationalize if appropriate. Sketch the angle in standard position to support your response.
34.
(5, –12 )
35.
(–6, –6)
36.
(–3, 5)
38.
csc θ > 0 and cosθ < 0
39.
sin θ < 0 and tanθ < 0
State the quadrant in which θ lies.
37.
cos θ > 0 and tanθ > 0
Without a calculator, find the exact values (if possible) of the remaining trigonometric functions of θ using
the
functional value and constraint.
Simplify & rationalize if appropriate. Sketch the angle in standard position to support your response.
40.
cos θ = −
42.
cot θ =
12
& θ lies in Quadrant III
13
4
and cosθ < 0
3
41.
sec θ = −2 and tanθ > 0
43.
sin θ =
−2
3π
and
< θ < 2π
3
2
Additional Review.
Convert the following degree measures to radians in exact form as a multiple of π, without the use of a calculator.
45. θ = 225°
46. θ = −120°
Convert each radian measure to degrees, without the use of a calculator.
5π
7π
48. θ = −
47. θ =
4
6
Convert each degree measure to radians. Use of a calculator is allowed, but show appropriate work.
Round to the nearest ten-thousandth. Use a graphing calculator to verify your results.
49. θ = 162°
50. −289.3°
Convert each radian measure to degrees. Use of a calculator is allowed, but show appropriate work.
Round to the nearest tenth. Use a graphing calculator to verify your results.
11π
52. θ = −6.432
51. θ =
10
Find a positive and a negative coterminal angle for each without the use of a calculator.
13π
53. θ = −340°
54. θ =
5
55. θ = 0.34
Find a coterminal angle in [0°, 360°] or [0, 2π] without the use of a calculator.
5π
56. θ = −
57. θ = 856°
8
If possible, find the complement of the angle without the use of a calculator.
58.
4π
9
59. θ = 2.6
60. θ = 32°
If possible, find the supplement of the angle without the use of a calculator.
61. θ = 181°
62. θ =
2π
5
63. θ = 3.13
Convert from degrees minutes seconds to decimal degrees or decimal degrees to degrees minutes and seconds. (Round
to the nearest thousandth for decimals and nearest second for degrees minutes and seconds)
64.
54°36'12''
65. 3.1415