Graph y=3sin(1/4x)

Problem

y=3*sin(1/4*x)

Solution

1. Identify the amplitude by looking at the coefficient a in the form y=a*sin(b*x) Here, a=3 so the amplitude is |3|=3 This means the graph oscillates between y=3 and y=−3

2. Determine the period using the formula P=(2*π)/b In this equation, b=1/4

P=(2*π)/(1/4)

P=8*π

3. Find the key points by dividing the period into four equal intervals. The interval width is (8*π)/4=2*π The xcoordinates for one cycle starting at x=0 are 0,2*π,4*π,6*π,8*π

4. Calculate the y-values for the key xcoordinates.

• At x=0 y=3*sin(0)=0

• At x=2*π y=3*sin(π/2)=3

• At x=4*π y=3*sin(π)=0

• At x=6*π y=3*sin(3*π/2)=−3

• At x=8*π y=3*sin(2*π)=0

5. Sketch the curve by plotting the points (0,0) (2*π,3) (4*π,0) (6*π,−3) and (8*π,0) and connecting them with a smooth sine wave.

Final Answer

To graph y=3*sin(1/4*x) plot a sine wave with amplitude 3 period 8*π and no phase shift.

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