Graph y=2cos(1/2x)

Problem

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

Solution

1. Identify the amplitude by looking at the coefficient a in the form y=a*cos(b*x) Here, a=2 so the amplitude is |2|=2 This means the graph oscillates between y=2 and y=−2

2. Determine the period using the formula P=(2*π)/b In this equation, b=1/2

P=(2*π)/(1/2)

P=4*π

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

4. Calculate the y-coordinates for these key points by substituting the xvalues into the function:

• At x=0 y=2*cos(0)=2

• At x=π y=2*cos(π/2)=0

• At x=2*π y=2*cos(π)=−2

• At x=3*π y=2*cos(3*π/2)=0

• At x=4*π y=2*cos(2*π)=2

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

Final Answer

y=2*cos(1/2*x)* has amplitude *2* and period *4*π

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