Graph y=1/4*sin(x)

Problem

y=1/4*sin(x)

Solution

1. Identify the parent function and its properties. The base 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 a=1/4 which means the amplitude is |a|=1/4 The graph will oscillate between y=1/4 and y=−1/4

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

4. Identify key points over one period [0,2*π] The standard five-point pattern for a sine wave (intercept, maximum, intercept, minimum, intercept) is applied using the new amplitude.

5. Calculate the coordinates for the key points:

• (0,0)

• (π/2,1/4)

• (π,0)

• ((3*π)/2,−1/4)

• (2*π,0)

6. Sketch the curve by plotting these points and connecting them with a smooth wave, then extending the pattern in both directions.

Final Answer

y=1/4*sin(x)

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