Graph y=2sin(x-pi/3)

Problem

y=2*sin(x−π/3)

Solution

1. Identify the amplitude by looking at the coefficient of the sine function. The amplitude is |A|=|2|=2 meaning the graph oscillates between y=2 and y=−2

2. Determine the period using the formula P=(2*π)/B Since the coefficient of x is B=1 the period is P=(2*π)/1=2*π

3. Find the phase shift by setting the argument of the sine function to zero. Solving x−π/3=0 gives a phase shift of π/3 to the right.

4. Calculate key points for one cycle by dividing the period into four equal intervals of (2*π)/4=π/2 Starting from the phase shift x=π/3 the key xvalues are π/3 (5*π)/6 (4*π)/3 (11*π)/6 and (7*π)/3

5. Plot the points and draw the sinusoidal curve. The points for one cycle are (π/3,0) ((5*π)/6,2) ((4*π)/3,0) ((11*π)/6,−2) and ((7*π)/3,0)

Final Answer

y=2*sin(x−π/3)

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