Graph y=3sin(2x)

Problem

y=3*sin(2*x)

Solution

1. Identify the amplitude by looking at the coefficient of the sine function. In the form y=A*sin(B*x) the amplitude is |A|

|A|=3

2. Determine the period of the function using the formula P=(2*π)/B Here, B=2

P=(2*π)/2=π

3. Find the key points by dividing the period into four equal intervals. The interval width is π/4

Intervals=0,π/4,π/2,(3*π)/4,π

4. Calculate the y-coordinates for each key point by substituting the x-values into the equation.

(0,0),(π/4,3),(π/2,0),((3*π)/4,−3),(π,0)

5. Sketch the graph by plotting these points and connecting them with a smooth sine wave that oscillates between y=3 and y=−3 over the interval [0,π]

Final Answer

y=3*sin(2*x)

(The graph is a sine wave with amplitude 3 period π and no phase shift.)

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