Graph sin(6x)

Problem

sin(6*x)

Solution

1. Identify the parent function and its properties. The function is of the form y=A*sin(B*x) where A=1 and B=6

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)/6=π/3

4. Find the horizontal scale by dividing the period into four equal intervals to identify key points (intercepts, maximums, and minimums).

Interval=(π/3)/4=π/12

5. Identify key coordinates over one period starting from x=0

(0,0)

(π/12,1)

(π/6,0)

(π/4,−1)

(π/3,0)

6. Sketch the curve by plotting these points and connecting them with a smooth wave that repeats every π/3 units along the x-axis.

Final Answer

Graph of *sin(6*x)* has amplitude *1* and period π/3

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