Graph y=7cos(x)

Problem

y=7*cos(x)

Solution

1. Identify the parent function and its properties. The base function is y=cos(x) which has a period of 2*π an amplitude of 1 and starts at a maximum point (0,1)

2. Determine the amplitude of the given function. The coefficient 7 in front of the cosine function indicates a vertical stretch. The amplitude is |7|=7

3. Determine the period and key points. Since the coefficient of x is 1 the period remains 2*π Key points occur every quarter-period, which is (2*π)/4=π/2

4. Calculate the coordinates for one full cycle.

• At x=0 y=7*cos(0)=7*(1)=7

• At x=π/2 y=7*cos(π/2)=7*(0)=0

• At x=π y=7*cos(π)=7*(−1)=−7

• At x=(3*π)/2 y=7*cos((3*π)/2)=7*(0)=0

• At x=2*π y=7*cos(2*π)=7*(1)=7

5. Sketch the graph by plotting these points (0,7) (π/2,0) (π,−7) ((3*π)/2,0) and (2*π,7) and connecting them with a smooth wave.

Final Answer

y=7*cos(x)

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