Graph y=-2sin(3x)

Problem

y=−2*sin(3*x)

Solution

1. Identify the amplitude. The amplitude is the absolute value of the coefficient of the sine function, |a|=|−2|=2 This means the graph oscillates between y=2 and y=−2

2. Determine the period. The period of a sine function y=a*sin(b*x) is calculated using the formula P=(2*π)/b Here, b=3 so the period is (2*π)/3

3. Identify 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. Determine the key points. Divide the period into four equal intervals of length (2*π)/3÷4=π/6 The xcoordinates for one cycle starting at x=0 are 0 π/6 π/3 π/2 and (2*π)/3

5. Calculate the y-coordinates. Evaluate the function at the key xvalues. Because of the negative sign in −2*sin(3*x) the graph is reflected across the xaxis.

(0,0)

(π/6,−2)

(π/3,0)

(π/2,2)

((2*π)/3,0)

6. Sketch the curve. Plot the key points and connect them with a smooth wave, repeating the pattern to extend the graph.

Final Answer

y=−2*sin(3*x)

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

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