Graph y=5cos(2x)

Problem

y=5*cos(2*x)

Solution

1. Identify the amplitude by looking at the coefficient in front of the cosine function. The amplitude is |A|=|5|=5 which means the graph oscillates between y=5 and y=−5

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 (2*π)/2=π

3. Calculate the phase shift and vertical shift. Since there are no horizontal or vertical translations added to the function, the phase shift is 0 and the vertical shift is 0

4. Find the key points by dividing the period into four equal intervals of length π/4 Starting from x=0 the xcoordinates are 0 π/4 π/2 (3*π)/4 and π

5. Evaluate the function at these key points to find the ycoordinates:

(0,5)

(π/4,0)

(π/2,−5)

((3*π)/4,0)

(π,5)

6. Sketch the curve by plotting these points and connecting them with a smooth, wave-like shape characteristic of a cosine graph.

Final Answer

y=5*cos(2*x)

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