Graph y=-3sin(x)

Problem

y=−3*sin(x)

Solution

1. Identify the parent function and its key characteristics. The base function is y=sin(x) which has a period of 2*π an amplitude of 1 and passes through the origin (0,0)

2. Determine the amplitude of the given function. The coefficient in front of the sine function is −3 The amplitude is the absolute value |−3|=3 meaning the graph will oscillate between y=3 and y=−3

3. Identify the reflection across the x-axis. Because the coefficient is negative, the graph of y=sin(x) is reflected vertically. Instead of starting by moving upward from the origin, the graph will move downward.

4. Determine the period of the function. The coefficient of x is 1 so the period remains 2*π The key points occur at intervals of (2*π)/4=π/2

5. Plot the key points over one period [0,2*π]

• At x=0 y=−3*sin(0)=0

• At x=π/2 y=−3*sin(π/2)=−3

• At x=π y=−3*sin(π)=0

• At x=(3*π)/2 y=−3*sin((3*π)/2)=3

• At x=2*π y=−3*sin(2*π)=0

6. Sketch the curve by connecting these points with a smooth wave.

Final Answer

To graph y=−3*sin(x) plot a sine wave with amplitude 3 period 2*π and a vertical reflection, passing through (0,0) (π/2,−3) (π,0) ((3*π)/2,3) and (2*π,0)

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