Graph y=6cos(x)

Problem

y=6*cos(x)

Solution

1. Identify the parent function and its properties. The parent function is y=cos(x) which has an amplitude of 1 and a period of 2*π

2. Determine the amplitude of the given function. The coefficient of the cosine function is 6 so the amplitude is |6|=6 This means the graph oscillates between y=6 and y=−6

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

4. Identify key points over one period [0,2*π]

• At x=0 y=6*cos(0)=6*(1)=6

• At x=π/2 y=6*cos(π/2)=6*(0)=0

• At x=π y=6*cos(π)=6*(−1)=−6

• At x=(3*π)/2 y=6*cos((3*π)/2)=6*(0)=0

• At x=2*π y=6*cos(2*π)=6*(1)=6

5. Sketch the curve by plotting these key points and connecting them with a smooth, wave-like shape, then extending the pattern in both directions.

Final Answer

y=6*cos(x)

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