What are the important points to graph $y = sin (3 x - \frac{π}{3})$ $y=sin(3x-pi/3)$ ?

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Answer 1 · 2018-08-06T04:39:45

As below.

Standard form of a sine function is $y = A sin (B x - C) + D$ $y = A sin (Bx - C) + D$

$Given y = sin (3 x - \frac{π}{3})$ $"Given " y = sin (3x - pi/3)$

$A = 1, B = 3, C = \frac{π}{3}, D = 0$ $A = 1, B = 3, C = pi/3, D = 0$

Important points to graph are Amplitude, Period, Phase Shift and Vertical Shift.

$A m p l i t u d e = | A | = 1$ $Amplitude = |A| = 1$

$"Period ' = (2pi) / |B| = (2pi) / 3$

$"Phase Shift " = -C / B = -9pi/3) / 3 = -pi/9, color(red)((pi/9) " to the LEFT"$

$"Vertical Shift " = D = 0$

graph{sin (3x - pi/3) [-10, 10, -5, 5]}

What are the important points to graph y=sin(3x-pi/3)y=sin(3x−π3)y=sin(3x-pi/3)?