Using transformation rules and your knowledge of trigonometric functions, draw the graph y=2sin(2x)

would use paper to show the student the final answer Your answer will be based around the graph of y=sin(x), which has a y maximum of 1 and minimum of -1, and one full cycle is completed by 2 pi. First y=2sin(x) will alter y=sin(x) by multiplying the graph by 2 in the y direction, so the graph will now have a y maximum of 2 and a minimum of -2. When you transform y=2sin(x) into y=2sin(2x), the x values are multiplied by the reciprocal of 2, which is 0.5. This will now mean that one full cycle of the sine wave will take just 1 pi.