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College Trigonometry, 2011a

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10.5 Graphs of the Trigonometric Functions 813<br />

(<br />

9. y =sin −x − π )<br />

− 2<br />

4<br />

Period: 2π<br />

Amplitude: 1<br />

Phase Shift: − π (You need to use<br />

( 4<br />

y = − sin x + π )<br />

− 2 to find this.) 15<br />

4<br />

− 9π 4 − 7π 4 − 5π 4 − 3π − π 4 4<br />

−1<br />

−2<br />

y<br />

π<br />

4<br />

3π<br />

4<br />

5π<br />

4<br />

7π<br />

4<br />

x<br />

Vertical Shift: −2<br />

−3<br />

10. y = 2 ( π<br />

)<br />

3 cos 2 − 4x +1<br />

π<br />

Period:<br />

2<br />

2<br />

Amplitude:<br />

3<br />

π<br />

Phase Shift: (You need to use<br />

8<br />

y = 2 (<br />

3 cos 4x − π 2<br />

Vertical Shift: 1<br />

)<br />

+ 1 to find this.) 16<br />

− 3π 8 − π 4 − π 8<br />

5<br />

3<br />

1<br />

1<br />

3<br />

y<br />

π<br />

8<br />

π<br />

4<br />

3π<br />

8<br />

π<br />

2<br />

5π<br />

8<br />

x<br />

11. y = − 3 (<br />

2 cos 2x + π )<br />

− 1 3 2<br />

Period: π<br />

Amplitude:<br />

3<br />

2<br />

Phase Shift: − π 6<br />

1<br />

− π 6− 1 2<br />

y<br />

π<br />

12<br />

π<br />

3<br />

7π<br />

12<br />

5π<br />

6<br />

x<br />

Vertical Shift: − 1 2<br />

−2<br />

12. y =4sin(−2πx + π)<br />

Period: 1<br />

Amplitude: 4<br />

1<br />

Phase Shift: (You need to use<br />

2<br />

y = −4sin(2πx − π) to find this.) 17<br />

Vertical Shift: 0<br />

− 1 2 − 1 4<br />

4<br />

y<br />

1<br />

4<br />

1<br />

2<br />

3<br />

4<br />

1 5<br />

4<br />

3<br />

2<br />

x<br />

−4<br />

15 Two cycles of the graph are shown to illustrate the discrepancy discussed on page 796.<br />

16 Again, we graph two cycles to illustrate the discrepancy discussed on page 796.<br />

17 This will be the last time we graph two cycles to illustrate the discrepancy discussed on page 796.

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