Graph y=-4sin(3x)

Problem

y=−4*sin(3*x)

Solution

1. Identify the amplitude. The amplitude is the absolute value of the coefficient of the sine function, |a|=|−4|=4 This means the graph oscillates between y=4 and y=−4

2. Determine the period. The period P is calculated using the formula P=(2*π)/|b| where b is the coefficient of x Here, b=3 so P=(2*π)/3

3. Find 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. Identify key points. Divide the period into four equal intervals of length P/4=(2*π)/12=π/6 The key xvalues are 0,π/6,π/3,π/2,(2*π)/3

5. Account for the reflection. The negative sign in front of the amplitude indicates a reflection across the xaxis. Instead of starting by going up, the sine wave will start by going down.

6. Calculate coordinates.

x=0⇒y=−4*sin(0)=0

x=π/6⇒y=−4*sin(π/2)=−4

x=π/3⇒y=−4*sin(π)=0

x=π/2⇒y=−4*sin((3*π)/2)=4

x=(2*π)/3⇒y=−4*sin(2*π)=0

Final Answer

y=−4*sin(3*x)

The graph is a sine wave with amplitude 4 period (2*π)/3 and no shifts, reflected across the xaxis.

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