Graph y=sin(8x)

Problem

y=sin(8*x)

Solution

1. Identify the parent function and its properties. The function is of the form y=A*sin(B*x) where the parent function is y=sin(x)

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

|A|=|1|=1

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

P=(2*π)/8

P=π/4

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

Phase Shift=0

Vertical Shift=0

5. Determine the key points for one cycle by dividing the period into four equal intervals. The interval width is π/4÷4=π/16

Point 1=(0,0)

Point 2=(π/16,1)

Point 3=(π/8,0)

Point 4=((3*π)/16,−1)

Point 5=(π/4,0)

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

Final Answer

y=sin(8*x)

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