Graph y=3cos(2pix)

Problem

y=3*cos(2*π*x)

Solution

1. Identify the amplitude by looking at the coefficient of the cosine function. The amplitude A is the absolute value of the leading coefficient.

A=|3|=3

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

P=(2*π)/(2*π)=1

3. Calculate the phase shift and vertical shift. Since there are no horizontal or vertical translations added to the function, both are zero.

Phase Shift=0

Vertical Shift=0

4. Find the key points for one cycle by dividing the period into four equal intervals. The interval width is 1/4=0.25 The xvalues are 0 0.25 0.5 0.75 and 1

x=0⇒y=3*cos(0)=3

x=0.25⇒y=3*cos(π/2)=0

x=0.5⇒y=3*cos(π)=−3

x=0.75⇒y=3*cos((3*π)/2)=0

x=1⇒y=3*cos(2*π)=3

5. Plot the points and draw a smooth wave. The graph oscillates between y=3 and y=−3 with a full cycle completed every 1 unit on the xaxis.

Final Answer

To graph y=3*cos(2*π*x) plot a cosine wave with amplitude 3 period 1 and no phase shift.

y=3*cos(2*π*x)

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