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Graph 5cos(x)

Problem

y=5*cos(x)

Solution

  1. Identify the parent function and its properties. The base 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 5 in front of the cosine function indicates a vertical stretch, making the amplitude |5|=5

  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 starting at x=0 The cosine function starts at its maximum value.

  • At x=0 y=5*cos(0)=5

  • At x=π/2 y=5*cos(π/2)=0

  • At x=π y=5*cos(π)=−5

  • At x=(3*π)/2 y=5*cos((3*π)/2)=0

  • At x=2*π y=5*cos(2*π)=5

  1. Sketch the curve by plotting these points and connecting them with a smooth, wave-like shape that oscillates between y=5 and y=−5

Final Answer

y=5*cos(x)

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