Graph y=sin(1/4x)

Problem

y=sin(1/4*x)

Solution

1. Identify the parent function and its parameters. The given function is in the form y=A*sin(B*x) where A=1 and B=1/4

2. Determine the amplitude, which is the absolute value of the coefficient A

|A|=|1|=1

3. Calculate the period using the formula P=(2*π)/B

P=(2*π)/(1/4)=8*π

4. Find the key points by dividing the period into four equal intervals of length (8*π)/4=2*π The xcoordinates for one cycle starting at the origin are 0 2*π 4*π 6*π and 8*π

5. Evaluate the function at these xvalues to find the corresponding ycoordinates.

At *x=0,y=sin(0)=0

At *x=2*π,y=sin(π/2)=1

At *x=4*π,y=sin(π)=0

At *x=6*π,y=sin((3*π)/2)=−1

At *x=8*π,y=sin(2*π)=0

6. Plot the points (0,0) (2*π,1) (4*π,0) (6*π,−1) and (8*π,0) and connect them with a smooth sine wave.

Final Answer

y=sin(1/4*x)* is a sine wave with amplitude 1 and period *8*π

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