Graph sin(1/2x)

Problem

y=sin(1/2*x)

Solution

1. Identify the parent function and its parameters. The function is in the form y=A*sin(B*x) where A=1 and B=1/2

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

|A|=|1|=1

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

P=(2*π)/(1/2)=4*π

4. Find the key points by dividing the period into four equal intervals of length π The xcoordinates for one cycle starting at the origin are 0 π 2*π 3*π and 4*π

5. Evaluate the function at these key points to find the ycoordinates.

sin(1/2⋅0)=0

sin(1/2⋅π)=1

sin(1/2⋅2*π)=0

sin(1/2⋅3*π)=−1

sin(1/2⋅4*π)=0

6. Plot the points (0,0) (π,1) (2*π,0) (3*π,−1) and (4*π,0) and connect them with a smooth sine wave.

Final Answer

y=sin(1/2*x)* has amplitude *1* and period *4*π

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