Graph y=3sin(2pix)

Problem

y=3*sin(2*π*x)

Solution

1. Identify the amplitude by looking at the coefficient of the sine function. The amplitude A is the absolute value of the multiplier in front of the sine.

|A|=3

2. Determine the period using the coefficient of x inside the sine function, which is B=2*π The formula for the period P is P=(2*π)/B

P=(2*π)/(2*π)=1

3. Find the key points by dividing the period into four equal intervals. Since the period is 1 the increments are 0.25 The xcoordinates for one cycle starting at the origin are 0 0.25 0.5 0.75 and 1

x=0,1/4,1/2,3/4,1

4. Calculate the y-coordinates for these key points. For a sine graph with no vertical or horizontal shifts, the pattern is: intercept, maximum, intercept, minimum, intercept.

(0,0),(0.25,3),(0.5,0),(0.75,−3),(1,0)

5. Sketch the graph by plotting these points and connecting them with a smooth, periodic wave. The graph oscillates between y=3 and y=−3 with a full cycle completed every 1 unit on the xaxis.

Final Answer

y=3*sin(2*π*x)

The graph is a sine wave with amplitude 3 period 1 and no phase shift.

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