Graphing trig
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This document contains graphs of trigonometric functions with various amplitudes, periods, and phase shifts. Each graph is defined by an equation and its amplitude, period, and phase shift are identified. Various trig functions are graphed, including sin, cos, tan, csc, and sec with different coefficients and phase angle shifts.
Graphing trig
- 1. 1p Parent Trig Graphs with translations
- 2. 1p
- 3. y = sin(2x) 1p
- 4. y = sin(2x) 1p
- 5. 1p y = sin(2x) Amplitude = 1 Period = π Phase shift = 0
- 6. y = 3sin(x) 1p
- 7. 1p y = 3sin(x) Amplitude = 3 Period = 2π Phase shift = 0
- 8. y = -4sin(2x) 1p
- 9. y = -4sin(2x) 1p Jeff Bivin -- LZHS
- 10. y = -4sin(2x) 1p Amplitude = 4 Period = π Phase shift = 0
- 11. y = sin(x + π/2) 1p x + π/2 = 0 x = -π/2 π/2
- 12. y = sin(x + π/2) 1p x + π/2 = 0 x = -π/2 π/2 Amplitude = 1 Period = 2π Phase shift = -π/2
- 13. ( ) cos 1 ö çè 1p ÷ø f x = æ x 2
- 14. ( ) cos 1 ö çè 1p ÷ø f x = æ x 2 Amplitude = 1 Period = 4π Phase shift = 0
- 15. (x) = cos(2 x) 1p f
- 16. (x) = cos(2 x) 1p f Amplitude = 1 Period = π Phase shift = 0
- 17. (x) = 3cos(2 x) 1p f
- 18. f (x) = 3cos(2 x) 1p Amplitude = 3 Period = π Phase shift = 0
- 19. f (x) 2cos x p 0 ö çè 1p ÷ø = æ - 3 x - p = 3 x = p 3 π/3
- 20. f (x) 2cos x p ö çè 1p Amplitude = 2 Period = 2π Phase shift = π/3 0 x - p = 3 x = p 3 ÷ø = æ - 3 π/3
- 21. (x) = 3cos(2x -p ) + 1 2x -p = 0 1p f x = p 2 π/2
- 22. (x) = 3cos(2x -p ) + 1 1p f UP 1 UP 1
- 23. (x) = 3cos(2x -p ) + 1 1p f UP 1 Amplitude = 3 Period = π Phase shift = π/2 UP 1
- 24. 1p
- 25. y = csc(x) 1 sin( x ) 1p y =
- 26. y = csc(x) 1 sin( x ) 1p Amplitude = 1 Period = 2π Phase shift = 0 y = Jeff Bivin -- LZHS
- 27. y = sec(x) 1 cos( x ) 1p y =
- 28. y = sec(x) 1 cos( x ) 1p y = Amplitude = 1 Period = 2π Phase shift = 0
- 29. 1p y = 3sec(x- π) x -p = 0 x =p π
- 30. 1p y = 3sec(x- π) x -p = 0 x =p π Amplitude = 3 Period = 2π Phase shift = π
- 31. 1p
- 32. y = tan(x) 1p y = x sin( ) x cos( ) Jeff Bivin -- LZHS
- 33. y = tan(x) 1p Amplitude = 1 Period = π Phase shift = 0
- 34. y = cot(x) 1p y = x cos( ) x sin( )
- 35. y = cot(x) 1p Amplitude = 1 Period = π Phase shift = 0
- 36. y = tan(2x+π) 1p y x = + p + sin(2 ) p x cos(2 ) 2x + p = 0 x = -p 2 π/2 Jeff Bivin -- LZHS
- 37. 1p y = tan(2x+π) 2x + p = 0 x = -p 2 π/2
- 38. 1p y = tan(2x+π) 2x + p = 0 x = -p 2 π/2 Amplitude = 1 Period = π/2 Phase shift = - π/2
- 39. 1p