Graph y=1/2cos(x)

Problem

y=1/2*cos(x)

Solution

1. Identify the parent function and its properties. The parent function is y=cos(x) which has an amplitude of 1 a period of 2*π and starts at a maximum point (0,1)

2. Determine the amplitude of the given function. The coefficient of the cosine term 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. Since the coefficient of x is 1 the period remains T=(2*π)/1=2*π

4. Identify key points for one full cycle. Divide the period into four equal intervals of π/2 to find the xcoordinates: 0,π/2,π,(3*π)/2,2*π

5. Calculate the ycoordinates for the key points:

• At x=0 y=1/2*cos(0)=1/2

• At x=π/2 y=1/2*cos(π/2)=0

• At x=π y=1/2*cos(π)=−1/2

• At x=(3*π)/2 y=1/2*cos((3*π)/2)=0

• At x=2*π y=1/2*cos(2*π)=1/2

6. Sketch the curve by plotting these points and connecting them with a smooth wave, repeating the pattern in both directions.

Final Answer

y=1/2*cos(x)

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