Graph y=4cos(2x)

Problem

y=4*cos(2*x)

Solution

1. Identify the amplitude by looking at the coefficient in front of the cosine function. The amplitude is |A|=|4|=4 which means the graph oscillates between y=4 and y=−4

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

3. Find the key points by dividing the period into four equal intervals. The interval width is 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. Since it is a cosine function, it starts at the maximum: (0,4) (π/4,0) (π/2,−4) ((3*π)/4,0) and (π,4)

5. Sketch the curve by plotting these points and connecting them with a smooth, wave-like shape. The pattern repeats every π units along the xaxis.

Final Answer

y=4*cos(2*x)

The graph is a cosine wave with amplitude 4 period π and no phase shift.

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