Graph y=3cos(1/2x)

Problem

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

Solution

1. Identify the amplitude by looking at the coefficient A in the form y=A*cos(B*x)

|A|=|3|=3

2. Calculate the period using the formula P=(2*π)/B where B=1/2

P=(2*π)/(1/2)=4*π

3. Determine the phase shift and vertical shift by observing the equation.

Phase Shift=0

Vertical Shift=0

4. Find the key points for one cycle by dividing the period into four equal intervals of length π

x=0⇒y=3*cos(0)=3

x=π⇒y=3*cos(π/2)=0

x=2*π⇒y=3*cos(π)=−3

x=3*π⇒y=3*cos((3*π)/2)=0

x=4*π⇒y=3*cos(2*π)=3

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

Final Answer

To graph y=3*cos(1/2*x) plot a cosine wave with amplitude 3 period 4*π starting at (0,3) and completing one cycle at (4*π,3)

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