Graph y=1/2*cos(2x)

Problem

y=1/2*cos(2*x)

Solution

1. Identify the amplitude by looking at the coefficient of the cosine function. The amplitude is |A|=1/2 which means the graph oscillates between y=1/2 and y=−1/2

2. Determine the period using the formula P=(2*π)/b where b is the coefficient of x Here, b=2

P=(2*π)/2=π

3. Calculate the key points by dividing the period into four equal intervals. The increment is π/4 The xcoordinates for one cycle starting at x=0 are 0,π/4,π/2,(3*π)/4,π

4. Evaluate the function at these key xvalues to find the corresponding ycoordinates.
   At x=0 y=1/2*cos(0)=1/2
   At x=π/4 y=1/2*cos(π/2)=0
   At x=π/2 y=1/2*cos(π)=−1/2
   At x=(3*π)/4 y=1/2*cos((3*π)/2)=0
   At x=π y=1/2*cos(2*π)=1/2

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

Final Answer

y=1/2*cos(2*x)

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