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Parent Trig Graphs

Learn how to apply translations, stretches, squeezes, flips to sine, cosine functions with examples and explanations.

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Parent Trig Graphs

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  1. Parent Trig Graphs with translations By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: October 11, 2005

  2. sine and cosine functions Jeff Bivin -- LZHS

  3. squeeze squeeze y = sin(2x) Jeff Bivin -- LZHS

  4. y = sin(2x) Jeff Bivin -- LZHS

  5. y = sin(2x) Amplitude = 1 Period = π Phase shift = 0 Jeff Bivin -- LZHS

  6. stretch stretch y = 3sin(x) Jeff Bivin -- LZHS

  7. y = 3sin(x) Amplitude = 3 Period = 2π Phase shift = 0 Jeff Bivin -- LZHS

  8. flip stretch squeeze stretch flip squeeze y = -4sin(2x) Jeff Bivin -- LZHS

  9. y = -4sin(2x) Jeff Bivin -- LZHS

  10. y = -4sin(2x) Amplitude = 4 Period = π Phase shift = 0 Jeff Bivin -- LZHS

  11. π/2 y = sin(x + π/2) x + π/2 = 0 x = -π/2 Jeff Bivin -- LZHS

  12. π/2 y = sin(x + π/2) x + π/2 = 0 x = -π/2 Amplitude = 1 Period = 2π Phase shift = -π/2 Jeff Bivin -- LZHS

  13. stretch Jeff Bivin -- LZHS

  14. Amplitude = 1 Period = 4π Phase shift = 0 Jeff Bivin -- LZHS

  15. squeeze squeeze Jeff Bivin -- LZHS

  16. Amplitude = 1 Period = π Phase shift = 0 Jeff Bivin -- LZHS

  17. stretch squeeze stretch squeeze Jeff Bivin -- LZHS

  18. Amplitude = 3 Period = π Phase shift = 0 Jeff Bivin -- LZHS

  19. stretch stretch π/3 Jeff Bivin -- LZHS

  20. π/3 Amplitude = 2 Period = 2π Phase shift = π/3 Jeff Bivin -- LZHS

  21. stretch squeeze stretch squeeze π/2 Jeff Bivin -- LZHS

  22. UP1 UP1 Jeff Bivin -- LZHS

  23. Amplitude = 3 Period = π Phase shift = π/2 UP1 UP1 Jeff Bivin -- LZHS

  24. secant and cosecant functions Jeff Bivin -- LZHS

  25. y = csc(x) Jeff Bivin -- LZHS

  26. y = csc(x) Amplitude = 1 Period = 2π Phase shift = 0 Jeff Bivin -- LZHS

  27. y = sec(x) y = cos(x) Jeff Bivin -- LZHS

  28. y = sec(x) Amplitude = 1 Period = 2π Phase shift = 0 Jeff Bivin -- LZHS

  29. stretch stretch y = 3sec(x-π) π Jeff Bivin -- LZHS

  30. y = 3sec(x-π) π Amplitude = 3 Period = 2π Phase shift = π Jeff Bivin -- LZHS

  31. tangent and cotangent functions Jeff Bivin -- LZHS

  32. y = tan(x) y = cos(x) Jeff Bivin -- LZHS

  33. y = tan(x) Amplitude = 1 Period = π Phase shift = 0 Jeff Bivin -- LZHS

  34. y = cot(x) y = sin(x) Jeff Bivin -- LZHS

  35. y = cot(x) Amplitude = 1 Period = π Phase shift = 0 Jeff Bivin -- LZHS

  36. squeeze squeeze y = tan(2x+π) π/2 y = cos(x) Jeff Bivin -- LZHS

  37. y = tan(2x+π) π/2 Jeff Bivin -- LZHS

  38. y = tan(2x+π) π/2 Amplitude = 1 Period = π/2 Phase shift = - π/2 Jeff Bivin -- LZHS

  39. THAT'S ALL FOLKS Jeff Bivin -- LZHS

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