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Trigo6_Horizontal Translation.ppt

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FernandoAvenir1

The document discusses the sine and cosine functions by showing their graphs over intervals of pi/2 between -2pi and 5pi/2. It explains that the sine function has a period of 2pi and repeats its pattern, while the cosine function is out of phase by pi/2. It also defines phase shift as a horizontal translation of trigonometric functions, where a negative value of C shifts the graph to the left and a positive C shifts it to the right.

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Trigo6_Horizontal Translation.ppt
THE AMPLITUDE OF THE SINE FUNCTION
THE PERIOD OF THE SINE FUNCTION
??? ????? ?? ???? ??? ? ???? ?? ???? ?? ? x y ?y = sin(x)
????? ?? ???? ??? ? ???? ?? ???? ?? ? x y
??? ????? ?? ???? ??? ? ???? ?? ???? ?? ? x y ?y = cos(x)
????? ?? ???? ??? ? ???? ?? ???? ?? ?? ?? ? x y
Trigo6_Horizontal Translation.ppt
Phase Shift ? A horizontal translation or shift of a trigonometric function ? y = Asin(B¦È ¨C C) or y = Acos(B¦È ¨C C) The phase shift is C/B, where B > 0 If C < 0, shifts to the left If C > 0, shifts to the right
Trigo6_Horizontal Translation.ppt

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Trigo6_Horizontal Translation.ppt

  • 2. THE AMPLITUDE OF THE SINE FUNCTION
  • 3. THE PERIOD OF THE SINE FUNCTION
  • 4. ??? ????? ?? ???? ??? ? ???? ?? ???? ?? ? x y ?y = sin(x)
  • 5. ????? ?? ???? ??? ? ???? ?? ???? ?? ? x y
  • 6. ??? ????? ?? ???? ??? ? ???? ?? ???? ?? ? x y ?y = cos(x)
  • 7. ????? ?? ???? ??? ? ???? ?? ???? ?? ?? ?? ? x y
  • 9. Phase Shift ? A horizontal translation or shift of a trigonometric function ? y = Asin(B¦È ¨C C) or y = Acos(B¦È ¨C C) The phase shift is C/B, where B > 0 If C < 0, shifts to the left If C > 0, shifts to the right