Graph y=2sin(2x)

Problem

y=2*sin(2*x)

Solution

1. Identify the amplitude by looking at the coefficient in front of the sine function.

A=|2|=2

2. Determine the period using the formula P=(2*π)/b where b is the coefficient of x

P=(2*π)/2=π

3. Calculate the phase shift and vertical shift. Since there are no constants added inside or outside the sine function, both are zero.

Phase Shift=0

Vertical Shift=0

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

x=0,π/4,π/2,(3*π)/4,π

5. Evaluate the function at these key xvalues to find the corresponding ycoordinates.

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

6. Sketch the graph by plotting these points and connecting them with a smooth wave, then extending the pattern in both directions.

Final Answer

y=2*sin(2*x)

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