More Lessons for Grade 11

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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 2pi. 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 2pi/B to find the period.

How the values of A and B affect the shape of the graph y = A sin(Bx).

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)).

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.

Example 1: 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.

Transformation of sin and cos with amplitude and vertical shift

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