How do you graph $y = 4 sin (x - \frac{π}{3}) + 2$ $y=4sin(x-pi/3)+2$ ?

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How do you graph $y = 4 sin (x - \frac{π}{3}) + 2$ $y=4sin(x-pi/3)+2$ ?

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Answer 1 · 2018-08-11T01:05:37

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Note: The two vertical lines are one period of the function placed at $x = \frac{π}{3}$ $x=pi/3$ and $x = \frac{7 π}{3}$ $x=(7pi)/3$ . Don't include the vertical lines when you graph it yourself, they are just visual aids.

Explanation:

First you must know the graph of the $sin$ $sin$ function.
graph{sinx [0, 6.282, -5, 5]}

Next find the amplitude, period, phase shift, and vertical shift.

Amplitude: 4 (function is four times higher
period: $2 π$ $2pi$ (nothing to change here)
phase shift: $\frac{π}{3}$ $pi/3$ to the right (change start point to the right $\frac{π}{3}$ $pi/3$ )
vertical shift: up 2 (shift the start point from ( $\frac{π}{3}$ $pi/3$ ,0 to $\frac{π}{3}$ $pi/3$ ,2)

Summary of translations: This is a sin function that has been shifted over $\frac{π}{3}$ $pi/3$ so one period of the function will go from $\frac{π}{3}$ $pi/3$ to $\frac{7 π}{3}$ $(7pi)/3$ (side note: $\frac{7 π}{3}$ $(7pi)/3$ = $(2 π + \frac{π}{3})$ $(2pi+pi/3)$ ). each point on the graph is multiplied by 4, because that is our amplitude. And it has been shifted up two units.

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How do you graph $y = 4 sin (x - \frac{π}{3}) + 2$ $y=4sin(x-pi/3)+2$ ?

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Explanation:

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