Chapter 5 Trigonometric Functions Answer Key 5.1 The Unit

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Transcript of Chapter 5 Trigonometric Functions Answer Key 5.1 The Unit

CK-12 PreCalculus Concepts 1
5.1 The Unit Circle
CK-12 PreCalculus Concepts 2
18. (Image from Wikipedia):
CK-12 PreCalculus Concepts 3
Answers
1.
2.
3. At multiples of 2π.
4. At values of (2 + 1) for all integer values of n.
5. −, 0, , 2
6.
-2
-1
1
2
x
y
CK-12 PreCalculus Concepts 4
-2
-1
1
2
x
y
9.
-2
-1
1
2
x
y
CK-12 PreCalculus Concepts 5
-2
-1
1
2
x
y
CK-12 PreCalculus Concepts 6
Answers
1. Amplitude is the value of a (it is always positive), that appears as the coefficient of sin or cos in the
equation.
2. Amplitude is the vertical distance between the sinusoidal axis and the maximum or minimum values
of the graph.
-4
-3
-2
-1
1
2
3
4
x
y
CK-12 PreCalculus Concepts 7
-4
-3
-2
-1
1
2
3
4
x
y
11.
-3π/2

-π/2
π/2
π
3π/2
x
y
CK-12 PreCalculus Concepts 8
-4
-3
-2
-1
1
2
3
4
x
y
13.
-4
-3
-2
-1
1
2
3
4
x
y
CK-12 PreCalculus Concepts 9
-1
1
x
y
15. The dotted horizontal line represents the sinusoidal axis at = 2.
-3π/2 -π -π/2 π/2 π 3π/2
-1
1
2
3
4
5
x
y
CK-12 PreCalculus Concepts 10
Answers
1.
-4
-2
2
4
6
8
x
y
2.
-1
1
x
y
3.
2
4
x
y
CK-12 PreCalculus Concepts 11
-1
1
2
x
y
5.
-4
-3
-2
-1
x
y
11. = −3 sin + 2
12. = −2 cos − 1
13. = 1
CK-12 PreCalculus Concepts 12
Answers
1. The frequency is 4 and the period is
2 .
2. The frequency is 2 and the period is .
3. The frequency is 1
2 and the period is 4.
4. The frequency is 3
4 and the period is
8
3 .
5. The frequency is 3 and the period is 2
3 .
6.
-2
2
4
x
y
CK-12 PreCalculus Concepts 13
-6
-4
-2
x
y
8.
-4
-2
xy
9.
-1.5
-1
-0.5
0.5
1
1.5
x
y
CK-12 PreCalculus Concepts 14
-4
-3
-2
-1
12. () = 2cos (2)
13. () = cos ( 1
6 ) + 6
CK-12 PreCalculus Concepts 15
Answers
1.
-4 -3 -2 -1
1 2 3 4
-4 -3 -2 -1
1 2 3 4
-4 -3 -2 -1
1 2 3 4
CK-12 PreCalculus Concepts 16
-4 -3 -2 -1
1 2 3 4
-4 -3 -2 -1
1 2 3 4
2 ) + 1
2 )
2 ) − 3
10. Possible answer: () = −2 cos ( −
2 ) + 1
2 ) − 3
720 ( − 180)) + 31
13. 39.69°
14. 28.67°
15. 565.5 minutes (about 9:26 AM); 1234.5 minutes (about 20:35 or 8:35 PM).
Chapter 5 – Trigonometric Functions Answer Key
CK-12 PreCalculus Concepts 17
Answers
1. You can use cos because sec = 1
cos .
2. You can use sin because csc = 1
sin .
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
CK-12 PreCalculus Concepts 18
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
5.
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
CK-12 PreCalculus Concepts 19
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
7.
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
CK-12 PreCalculus Concepts 20
8.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
9.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
CK-12 PreCalculus Concepts 21
10.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
11.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
x
y
CK-12 PreCalculus Concepts 22
-3
-2
-1
1
2
3
x
y
13.
-3
-2
-1
1
2
3
x
y
CK-12 PreCalculus Concepts 23

2 )

2 )
CK-12 PreCalculus Concepts 24
Answers
1.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
CK-12 PreCalculus Concepts 25
2.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
CK-12 PreCalculus Concepts 26
8.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
9.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
CK-12 PreCalculus Concepts 27
10.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
11.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
CK-12 PreCalculus Concepts 28
12.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
13.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
CK-12 PreCalculus Concepts 29
14.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
15.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-7π/2
-3π
-5π/2
-2π
-3π/2

-π/2
π/2
x
y
CK-12 PreCalculus Concepts 30
16.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-π/2
π/2
π
3π/2

5π/2
x
y
17.
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-3π/2

-π/2
π/2
π
3π/2
x
y
CK-12 PreCalculus Concepts 31