Math III Honors

Name___________________________________

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Graphing Sine and Cosine

Date________________ Period____

1) sin x

2) cos x y

y

2

2

1.5

1.5

1

1

0.5

0.5

π 2

−0.5

π

3π 2

2π

5π 2

3π

7π 2

4π

−2π

x

−

3π −π 2

−

π 2−0.5

−1

−1

−1.5

−1.5

−2

−2

π 2

π

3π 2

2π

x

Define the Following and List the formula to find it. 3) Amplitude

4) Period

5) Cycle

6) Frequency

7) Frequency

Using radians, find the amplitude and period of each function. Then graph. 8) y =

9) y = 2sin 2θ

1 θ ⋅ sin 2 3

6 5 6

4

5

3

4

2

3

1

2 1

−1 π

2π

3π

4π

5π

6π

7π

8π

π 2

π

3π 2

2π

−2

9π

−1

−3

−2

−4

−3

−5

−4

−6

−5 −6

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10) y = 4sin 2θ

11) y = sin 4θ

6

6

5

5

4

4

3

3

2

2

1

1 π 2

−1

π

3π 2

2π

π 2

−1

−2

−2

−3

−3

−4

−4

−5

−5

−6

−6

12) y = 4cos 2θ

13) y = cos

π

3π 2

2π

θ 4

6 5 6 4 5 3 4 2 3 1 2 π 2

−1

π

3π 2

2π

1 π 2π 3π 4π 5π 6π 7π 8π 9π 10π 11π 12π

−2 −1 −3 −2 −4 −3 −5 −4 −6 −5 −6

14) y =

1 θ ⋅ cos 2 2

15) y = cos

θ 3

6 6 5 5 4 4 3 3 2 2 1 1 π π

2π

3π

4π

5π

6π

2π

3π

4π

5π

6π

7π

8π

9π

−1

−1 −2 −2 −3 −3 −4 −4 −5 −5 −6 −6

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16) y = 2sin 3θ

17) y = 4sin 2θ

6

6

5

5

4

4

3

3

2

2

1

1 π 2

−1

π

3π 2

2π −1

−2

−2

−3

−3

−4

−4

−5

−5

−6

−6

18) y = 3cos θ

6

5

5

4

4

3

3

2

2

1

1 π 2

π

π

3π 2

2π

π

3π 2

2π

3π 2

2π

19) y = 2sin 4θ

6

−1

π 2

3π 2

2π

5π 2

3π −1

−2

−2

−3

−3

−4

−4

−5

−5

−6

−6

20) y = 3sin 3θ

21) y =

π 2

1 ⋅ sin 2θ 2

6 5 4

6

3

5

2

4

1

3 2

−1

π 2

π

3π 2

2π 1

−2 −3

−1

−4

−2

−5

−3

−6

−4

π 2

π

−5 −6

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Worksheet by Kuta Software LLC

(

22) y = cos θ +

7π 4

)

( )

23) y = sin θ +

6

6

5

5

4

4

3

3

2

2

1

1

−1

π 2

π

3π 2

2π

5π 2

3π −1

−2

−2

−3

−3

−4

−4

−5

−5

−6

−6

(

24) y = cos θ −

11π 6

)

6 5

4

4

3

3

2

2

1

1 π

3π 2

2π

5π 2

3π −1

−2

−2

−3

−3

−4

−4

−5

−5

−6

−6

( )

26) y = cos θ +

6 5

4

4

3

3

2

2

1

1 π

3π 2

π

27) y = sin θ +

5

π 2

π 2

(

π 4

6

−1

2π

3π 2

2π

5π 2

3π

2π

5π 2

3π

2π

5π 2

3π

( )

5

π 2

π

25) y = sin θ −

6

−1

π 2

π 3

5π 2

3π −1

−2

−2

−3

−3

−4

−4

−5

−5

−6

−6

π 2

π

π 2

3π 2

3π 2

3π 2

)

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28) y =

29) y = 2cos 4θ − 2

1 ⋅ cos θ + 2 2

6 5 6

4

5

3

4

2

3

1

2 −

1 π 2

−1

π

3π 2

2π

5π 2

3π

π 4 −1 −2

π 4

π 2

3π 4

π

5π 3π 7π 2π 4 2 4

−3

−2

−4

−3

−5

−4

−6

−5 −6

30) y = 2sin 3θ − 1

−

31) y = −2 + 3sin θ

6

6

5

5

4

4

3

3

2

2

1

1

π 4 −1 −2

π 4

π 2

3π 4

π

5π 3π 7π 2π 4 2 4

π

3π 2

2π

5π 2

3π

−2

−3

−3

−4

−4

−5

−5

−6

−6

32) y =

π 2

−1

1 θ ⋅ sin + 1 2 4

33) y = 3cos

θ +1 2

6 6 5 5 4 4 3 3 2 2 1 1 π π 2π 3π 4π 5π 6π 7π 8π 9π 10π 11π 12π

2π

3π

4π

5π

6π

−1

−1 −2 −2 −3 −3 −4 −4 −5 −5 −6 −6

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