Graph y=sin(1/2x)

Problem

y=sin(1/2*x)

Solution

1. Identify the parent function and its properties. The function is of the form y=A*sin(B*x) where A is the amplitude and B affects the period.

2. Determine the amplitude. The coefficient A is 1 so the amplitude is |1|=1 The graph oscillates between y=1 and y=−1

3. Calculate the period. The period P of a sine function is given by P=(2*π)/B Here, B=1/2

P=(2*π)/(1/2)

P=4*π

4. Find the key points for one full cycle. Divide the period into four equal intervals of length (4*π)/4=π

• Start: (0,0)

• Quarter point: (π,1)

• Midpoint: (2*π,0)

• Three-quarter point: (3*π,−1)

• End: (4*π,0)

5. Sketch the curve by plotting these key points and connecting them with a smooth wave, then extend the pattern in both directions.

Final Answer

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

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