Graph y=2sin(5x)

Problem

y=2*sin(5*x)

Solution

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

|A|=2

2. Determine the period of the function using the formula P=(2*π)/B Here, B=5

P=(2*π)/5

3. Calculate the phase shift and vertical shift. Since there are no horizontal or vertical translations added to the argument or the 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 P/4=(2*π)/20=π/10

x=0,π/10,(2*π)/10,(3*π)/10,(4*π)/10

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

(0,0),(π/10,2),(π/5,0),((3*π)/10,−2),((2*π)/5,0)

6. Sketch the graph by plotting these points and connecting them with a smooth sine wave, oscillating between y=2 and y=−2

Final Answer

y=2*sin(5*x)

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