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Graph y=8sin(x)

Problem

y=8*sin(x)

Solution

  1. Identify the parent function and its properties. The parent function is y=sin(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 sine function 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. Since the coefficient of x is 1 the period remains 2*π

  4. Identify key points over one period [0,2*π] The sine function starts at the origin, reaches its maximum, returns to zero, reaches its minimum, and returns to zero.

  • At x=0 y=8*sin(0)=0

  • At x=π/2 y=8*sin(π/2)=8

  • At x=π y=8*sin(π)=0

  • At x=(3*π)/2 y=8*sin((3*π)/2)=−8

  • At x=2*π y=8*sin(2*π)=0

  1. Sketch the curve by plotting these key points and connecting them with a smooth wave. The graph repeats this pattern every 2*π units along the x-axis.

Final Answer

y=8*sin(x)

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