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Graph y=7sin(x)

Problem

y=7*sin(x)

Solution

  1. Identify the parent function and its properties. The base function is y=sin(x) which has a period of 2*π an amplitude of 1 and passes through the origin (0,0)

  2. Determine the amplitude of the given function. The coefficient of the sine function is 7 which means the amplitude is |7|=7 This stretches the graph vertically, so the maximum value is 7 and the minimum value is −7

  3. Determine the period of the function. Since the coefficient of x is 1 the period remains 2*π The graph completes one full cycle between x=0 and x=2*π

  4. Identify key points for one period. Divide the period into four equal intervals to find the intercepts, maximums, and minimums:

  • At x=0 y=7*sin(0)=0

  • At x=π/2 y=7*sin(π/2)=7

  • At x=π y=7*sin(π)=0

  • At x=(3*π)/2 y=7*sin((3*π)/2)=−7

  • At x=2*π y=7*sin(2*π)=0

  1. Sketch the curve by plotting these points and connecting them with a smooth wave. The graph oscillates between y=7 and y=−7 every 2*π units along the x-axis.

Final Answer

y=7*sin(x)

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