Honors Algebra 2 Name

Honors Algebra 2 13.4 Sine and Cosine Graphs Worksheet

Name ________________________________________ Date________________ Hour _____________

For each function, state the amplitude, if there is a reflection, the phase shift and the vertical shift. Write "none" for

transformations that do not exist.

Then graph the function.

Step #1: Start by graphing the parent function =

if there is no period change (b).

If there is a period change, find the new intervals first, then graph the parent graph as usual.

Step #2: Write the transformations IN THE ORDER IN WHICH THEY OCCUR

Step #3: Graph each transformation ? one at a time, use more than one color!!!

Step #4: Label your final graph.

1. = sin

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

2. = 4 sin

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

3. = 2sin

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

4. = sin + 3

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

5. = sin - 4

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

6. = sin -

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

7. = - sin + 3

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

8. = -2 sin( - )

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

9. = 4 sin -

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

10. = - sin + + 1

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

11. = 3 sin( + ) - 2

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

12. = cos

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

13. = cos

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

14. = 3 cos

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

15. = cos - 5

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

16. = cos - + 2

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

17. = 3 cos 2 - 1 Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

18. = - cos - 2 Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

19. = - cos( - ) - 1 Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

20. = 3 cos + - 2

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

21. = -2 cos 2( - ) + 1

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

22. = cos( + 2 ) + 3

Period: __________ Amplitude:_______ Reflection:_______ Phase Shift:__________ Vertical Shift:__________ Transformations:

Directions: Match the graph with its equation by writing the appropriate letter next to the equation.

23. y 4 sin 4x

________

24. y cos x

________

D.

25. y 4 cos 4x

________

1 26. y 4 sin x

4

________

E.

F.

27. y sin 2 x ________

2

28. y cos x 2

________

1

G.

29. y cos x 1 ________

2

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