Trigonometric Transformations: Sine
The Transformation of the Sine Graph Students will be able to understand how a sine graph transforms. Students should already know what the graph of f(x) = sin(x) looks like. When given 2sin(x), or sin(2x-(1/2)) students will not be able to graph. This geogebra allows students to manipulate the amplitude, period, phase shift and midline of a sine graph. By doing so students will be able to graph the above graphs after this activity.
Ask students what the graph sin(x) looks like. Show students the formula used to determine the transformations of graphs, which is, A*(sin(Bx-C))+D. Where A is the amplitude, B is used to find the period, C is the phase shift and D is the midline. HINT: When answering questions, use point E as a reference point. When B is increased/decreased what happens to the graph? What happens when B = 0? What happens when A is greater than 0? What happens at A =1,2,3...etc What happens when A is less than 0? at A = -1,-2,-3 What happens when A = 0? What is happening to the graph when C is increased? If we went from C= 1 to C=3, what change(s) occurred? What is happening to the graph when C is decreased? If we went from C=1 to C=-2, what change(s) occurred to the graph? What happens when D is increased? What change occurs from when D=0, to when D=2? What happens when D is decreased from D=0 to D=-3? If I gave you f(x)=2sin(x-1)+3, what do you think the graph would look like?