Graph y=6sin(x)

Problem

y=6*sin(x)

Solution

1. Identify the parent function and its properties. The function is a transformation of y=sin(x) which has a period of 2*π and oscillates between −1 and 1

2. Determine the amplitude of the function. The coefficient 6 in front of the sine function indicates a vertical stretch. The amplitude is |6|=6

3. Determine the period of the function. Since the coefficient of x is 1 the period remains 2*π

4. Identify key points over one period [0,2*π] The sine function starts at the midline, goes to the maximum, returns to the midline, goes to the minimum, and returns to the midline.

• At x=0 y=6*sin(0)=0

• At x=π/2 y=6*sin(π/2)=6

• At x=π y=6*sin(π)=0

• At x=(3*π)/2 y=6*sin((3*π)/2)=−6

• At x=2*π y=6*sin(2*π)=0

5. Sketch the curve by plotting these points and connecting them with a smooth wave. The graph oscillates between y=6 and y=−6

Final Answer

y=6*sin(x)

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