Graph y=1/2*sin(x)

Problem

y=1/2*sin(x)

Solution

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

2. Determine the amplitude of the given function. The coefficient of the sine function is a=1/2 so the amplitude is |a|=1/2 This means the graph oscillates between y=1/2 and y=−1/2

3. Determine the period of the function. The coefficient of x is 1 so the period is T=(2*π)/1=2*π

4. Identify key points over one period [0,2*π] Divide the period into four equal intervals to find the xintercepts, maximums, and minimums:

• At x=0 y=1/2*sin(0)=0

• At x=π/2 y=1/2*sin(π/2)=1/2

• At x=π y=1/2*sin(π)=0

• At x=(3*π)/2 y=1/2*sin((3*π)/2)=−1/2

• At x=2*π y=1/2*sin(2*π)=0

5. Sketch the curve by plotting these points and connecting them with a smooth wave. The graph is a vertical compression of the standard sine wave by a factor of 1/2

Final Answer

y=1/2*sin(x)

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