Graph y=-3sin(2x)

Problem

y=−3*sin(2*x)

Solution

1. Identify the amplitude. The amplitude is the absolute value of the coefficient of the sine function, |a|=|−3|=3 This means the graph oscillates between y=3 and y=−3

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

3. Find the phase shift and vertical shift. Since there are no horizontal or vertical translations added to the argument or the 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 π/4 Starting from x=0 the key xvalues are 0,π/4,π/2,(3*π)/4,π

5. Calculate the y-coordinates. Evaluate the function at the key xvalues:

• At x=0 y=−3*sin(0)=0

• At x=π/4 y=−3*sin(π/2)=−3

• At x=π/2 y=−3*sin(π)=0

• At x=(3*π)/4 y=−3*sin((3*π)/2)=3

• At x=π y=−3*sin(2*π)=0

6. Reflect and plot. Because the coefficient a is negative, the graph is a reflection of y=3*sin(2*x) across the xaxis, starting by moving downward from the origin.

Final Answer

To graph y=−3*sin(2*x) plot the points (0,0) (π/4,−3) (π/2,0) ((3*π)/4,3) and (π,0) then connect them with a smooth wave.

Amplitude=3,Period=π

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