Transform sine and cosine functions by changing the values of a, h, and k,

Transform sine and cosine functions by changing the values of a, h, and k,
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  • Sine FunctionThe Equation is: y=a(sin)[b(x-h)]+k
  • This is true because in this case, "a" is the amplitude , "p" is the period and the "h" is the horizontal shift.
  • You're right. But you forgot "k". "k" is the vertical shift
  • Cosine FunctionThe equation is y=a(cos)[b(x-h)]+k
  • As you can see there is a difference between Sine and Cosine. The parent function for Sine starts on zero . Cosine starts on the y-axis. But there can also be shifts in the graphs. For example if h is π/2 then you starts on that on the x axis. If k is 2 then you shift the graph vertically up 2 units.
  • example of sine y=-0.2sin(0.5x)+0.1
  • What are the steps for graphing?
  • -2 -3
  • 1 -1
  • -3 0
  • 1) Find the values for domain and range2) Calculate the graphs x-intercept and Period3) Calculate the graph's minimums and maximum points4) Once you have done all of that you sketch the graph of the function
  • 2pi/3 3
  • Example of cosiney=2cos(x-pi)-1
  • 4pi 3
  • 2pi 3
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