Graph y=sin(1/5x)

Problem

y=sin(1/5*x)

Solution

1. Identify the parent function and its parameters. The given function is in the form y=A*sin(B*x) where A=1 and B=1/5

2. Determine the amplitude, which is the absolute value of the coefficient A

|A|=|1|=1

3. Calculate the period of the function using the formula P=(2*π)/|B|

P=(2*π)/(1/5)=10*π

4. Find the phase shift and vertical shift. Since there are no horizontal or vertical translations added to the argument or the function, both the phase shift and vertical shift are 0

5. Determine the key points for one cycle by dividing the period into four equal intervals of length (10*π)/4=2.5*π The xcoordinates are 0 2.5*π 5*π 7.5*π and 10*π

6. Evaluate the function at these key points to find the ycoordinates:

(0,0)

(2.5*π,1)

(5*π,0)

(7.5*π,−1)

(10*π,0)

7. Sketch the graph by plotting these points and drawing a smooth sine wave through them, repeating the pattern in both directions.

Final Answer

y=sin(1/5*x)* has amplitude *1* and period *10*π

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