Graph y=2sin(4x)

Problem

y=2*sin(4*x)

Solution

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

|A|=2

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

b=4

P=(2*π)/4=π/2

3. Calculate the phase shift and vertical shift. Since there are no constants added inside or outside the sine function, both shifts 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/2÷4=π/8

x=0,π/8,π/4,(3*π)/8,π/2

5. Evaluate the y-coordinates at these key points to plot the graph.

y(0)=2*sin(0)=0

y(π/8)=2*sin(π/2)=2

y(π/4)=2*sin(π)=0

y((3*π)/8)=2*sin((3*π)/2)=−2

y(π/2)=2*sin(2*π)=0

Final Answer

y=2*sin(4*x)

The graph is a sine wave with amplitude 2 period π/2 and key points at (0,0) (π/8,2) (π/4,0) ((3*π)/8,−2) and (π/2,0)

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