 # Transformation of Sine and Cosine Graphs

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Examples, videos, worksheets, solutions, and activities to help Algebra 2 students learn how to transform sine and cosine graphs.

Sine and Cosine Transformations
The coefficients A and B in y = Asin(Bx) or y = Acos(Bx) each have a different effect on the graph. If A and B are 1, both graphs have an amplitude of 1 and a period of 2π. For sine and cosine transformations, when A is larger than 1, the amplitude increases and is equal to the value of A; if A is negative, the graph reflects over the x-axis. When B is greater than 1, the period decreases; use the formula 2π/B to find the period.

How the values of A and B affect the shape of the graph y = A sin(Bx)?
More Transformations of Sine and Cosine
In the equation y=Asin(B(x-h)), A modifies the amplitude and B modifies the period; see sine and cosine transformations. The constant h does not change the amplitude or period (the shape) of the graph. It shifts the graph left (if h is negative) or right (if h is positive) and in the amount equal to h. The amount of horizontal shift is called the phase shift, which equals h.

How the value of h affects the shape of the graph y = A sin(B(x-h))?

Graphing Sine or Cosine Functions with Different Coefficients
Graph Sine and Cosine in the form y = Asin(B(x-D))+C and y = Acos(B(x-d))+C
Graph Sine and Cosine with the four basic transformations.
State Amplitude, Period, Phase shift and Vertical shift.
How to determine the horizontal and vertical translations of sine and cosine?
How to graph translated sine and cosine functions? Example 1: This video provides an example of describing and graphing a transformation of the sine and cosine functions. Example 2: This video provides an example of describing and graphing a transformation of the sine and cosine functions. Example 3: This video provides an example of describing and graphing a transformation of the sine and cosine functions. Example 4: This video provides an example of describing and graphing a transformation of the sine and cosine functions. Transformation of sin and cos with amplitude and vertical shift

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