Graph 2cos(x)

Problem

y=2*cos(x)

Solution

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

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

3. Determine the period of the function. Since the coefficient of x is 1 the period remains 2*π

4. Identify key points for one full cycle from x=0 to x=2*π

• At x=0 y=2*cos(0)=2*(1)=2

• At x=π/2 y=2*cos(π/2)=2*(0)=0

• At x=π y=2*cos(π)=2*(−1)=−2

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

• At x=2*π y=2*cos(2*π)=2*(1)=2

5. Sketch the curve by plotting these points and connecting them with a smooth wave. The graph oscillates between y=2 and y=−2

Final Answer

To graph y=2*cos(x) plot a cosine wave with an amplitude of 2 and a period of 2*π starting at (0,2)

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