Graph y=5sin(x)

Problem

y=5*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 5 so the amplitude is |5|=5 This means the graph will oscillate between a maximum of y=5 and a minimum of y=−5

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 over the interval [0,2*π]

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

• At x=0 y=5*sin(0)=0 Point: (0,0)

• At x=π/2 y=5*sin(π/2)=5*(1)=5 Point: (π/2,5)

• At x=π y=5*sin(π)=0 Point: (π,0)

• At x=(3*π)/2 y=5*sin((3*π)/2)=5*(−1)=−5 Point: ((3*π)/2,−5)

• At x=2*π y=5*sin(2*π)=0 Point: (2*π,0)

5. Sketch the curve by connecting these points with a smooth wave. The graph is a vertical stretch of the standard sine wave by a factor of 5

Final Answer

y=5*sin(x)

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