Graph y=1/3*cos(2x)

Problem

y=1/3*cos(2*x)

Solution

1. Identify the amplitude by looking at the coefficient of the cosine function. The amplitude is |a|=1/3 which means the graph oscillates between y=1/3 and y=−1/3

2. Determine the period using the formula P=(2*π)/b where b=2

P=(2*π)/2=π

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

4. Calculate the y-coordinates for these key points using the function y=1/3*cos(2*x)

• At x=0 y=1/3*cos(0)=1/3

• At x=π/4 y=1/3*cos(π/2)=0

• At x=π/2 y=1/3*cos(π)=−1/3

• At x=(3*π)/4 y=1/3*cos((3*π)/2)=0

• At x=π y=1/3*cos(2*π)=1/3

5. Plot the points and draw a smooth wave. The graph is a cosine wave with a maximum at (0,1/3) intercepts at (π/4,0) and ((3*π)/4,0) and a minimum at (π/2,−1/3)

Final Answer

y=1/3*cos(2*x)* has amplitude 1/3* and period *π

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