Graph y=8cos(x)

Problem

y=8*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 term is 8 so the amplitude is |8|=8 This means the graph oscillates between y=8 and y=−8

3. Determine the period of the function. The coefficient of x is 1 so the period remains T=(2*π)/1=2*π

4. Identify key points for one full cycle starting at x=0

• At x=0 y=8*cos(0)=8*(1)=8

• At x=π/2 y=8*cos(π/2)=8*(0)=0

• At x=π y=8*cos(π)=8*(−1)=−8

• At x=(3*π)/2 y=8*cos((3*π)/2)=8*(0)=0

• At x=2*π y=8*cos(2*π)=8*(1)=8

5. Sketch the graph by plotting these key points and connecting them with a smooth, periodic wave.

Final Answer

y=8*cos(x)

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