Graph y=1/3*sin(x)

Problem

y=1/3*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=1/3 This means the graph is vertically compressed, and the maximum and minimum values are 1/3 and −1/3 respectively.

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

4. Identify key points over one period [0,2*π] The sine function starts at the origin, reaches its maximum, returns to zero, reaches its minimum, and returns to zero.

• At x=0 y=1/3*sin(0)=0

• At x=π/2 y=1/3*sin(π/2)=1/3

• At x=π y=1/3*sin(π)=0

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

• At x=2*π y=1/3*sin(2*π)=0

5. Sketch the graph by plotting these key points and connecting them with a smooth wave. The graph oscillates between y=1/3 and y=−1/3 every 2*π units.

Final Answer

y=1/3*sin(x)

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