Graph y=-5cos(2x)

Problem

y=−5*cos(2*x)

Solution

1. Identify the amplitude by taking the absolute value of the coefficient of the cosine function.

|A|=|−5|=5

2. Determine the period of the function using the formula P=(2*π)/b where b=2

P=(2*π)/2=π

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

Phase Shift=0

Vertical Shift=0

4. Find the key points by dividing the period into four equal intervals of π/4

x=0,π/4,π/2,(3*π)/4,π

5. Evaluate the function at these key points. Because the coefficient is negative, the graph starts at a minimum.

y(0)=−5

y(π/4)=0

y(π/2)=5

y((3*π)/4)=0

y(π)=−5

6. Sketch the curve by plotting these points and connecting them with a smooth wave starting at (0,−5) reaching a peak at (π/2,5) and returning to the minimum at (π,−5)

Final Answer

y=−5*cos(2*x)

The graph is a cosine wave with amplitude 5 period π and no phase shift, reflected across the x-axis.

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