Graph y=3sin(3x)

Problem

y=3*sin(3*x)

Solution

1. Identify the amplitude by looking at the coefficient in front of the sine function. The amplitude is |3| which means the graph oscillates between y=3 and y=−3

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

P=(2*π)/3

3. Calculate the phase shift and vertical shift. Since there are no constants added inside or outside the sine function, the phase shift is 0 and the vertical shift is 0

4. Find the key points by dividing the period into four equal intervals of length P/4

Interval=(2*π/3)/4=π/6

5. Evaluate the function at the five key xvalues within one period starting from x=0

x=0⇒y=3*sin(0)=0

x=π/6⇒y=3*sin(π/2)=3

x=π/3⇒y=3*sin(π)=0

x=π/2⇒y=3*sin((3*π)/2)=−3

x=(2*π)/3⇒y=3*sin(2*π)=0

6. Sketch the curve by plotting these points (0,0) (π/6,3) (π/3,0) (π/2,−3) and ((2*π)/3,0) and connecting them with a smooth wave.

Final Answer

y=3*sin(3*x)

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