1. Lake Zurich High School
Parent Trig Graphs
with translations
By: Jeffrey Bivin
Lake Zurich High School
Last Updated: October 11, 2005

2. sine
and
cosine
functions
Jeff Bivin -- LZHS

3. y = sin(2x)
squeeze
squeeze
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4. y = sin(2x)
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5. y = sin(2x) Amplitude = 1 Period = π Phase shift = 0
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6. y = 3sin(x)
stretch
stretch
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7. y = 3sin(x) Amplitude = 3 Period = 2π Phase shift = 0
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8. y = -4sin(2x)
flip
stretch
squeeze
squeeze
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9. y = -4sin(2x)
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10. y = -4sin(2x) Amplitude = 4 Period = π Phase shift = 0
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11. y = sin(x + π/2)
x + π/2 = 0
x = -π/2
π/2
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12. y = sin(x + π/2) x + π/2 = 0 x = -π/2 π/2 Amplitude = 1 Period = 2π
Phase shift = -π/2
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13. stretch
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14. Amplitude = 1
Period = 4π
Phase shift = 0
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15. squeeze
squeeze
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16. Amplitude = 1
Period = π
Phase shift = 0
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17. stretch
squeeze
squeeze
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18. Amplitude = 3
Period = π
Phase shift = 0
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19. π/3
stretch
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20. π/3
Amplitude = 2
Period = 2π
Phase shift = π/3
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21. π/2
stretch
squeeze
squeeze
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22. UP 1
UP 1
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23. UP 1 UP 1 Amplitude = 3 Period = π Phase shift = π/2
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24. secant
and
cosecant
functions
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25. y = csc(x)
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26. y = csc(x) Amplitude = 1 Period = 2π Phase shift = 0
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27. y = sec(x)
y = cos(x)
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28. y = sec(x) Amplitude = 1 Period = 2π Phase shift = 0
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29. y = 3sec(x-π) π
stretch
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30. y = 3sec(x-π) π Amplitude = 3 Period = 2π Phase shift = π
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31. tangent
and
cotangent
functions
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32. y = tan(x)
y = cos(x)
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33. y = tan(x)
Amplitude = 1
Period = π
Phase shift = 0
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34. y = cot(x)
y = sin(x)
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35. y = cot(x)
Amplitude = 1
Period = π
Phase shift = 0
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36. y = tan(2x+π)
π/2
y = cos(x)
squeeze
squeeze
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37. y = tan(2x+π)
π/2
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38. y = tan(2x+π) π/2 Amplitude = 1 Period = π/2 Phase shift = - π/2
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39. THAT'S
ALL
FOLKS
Jeff Bivin -- LZHS