How do you use transformation to graph the sin function and determine the amplitude and period of $y = sin (x + \frac{π}{6})$ $y=sin(x+pi/6)$ ?

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How do you use transformation to graph the sin function and determine the amplitude and period of $y = sin (x + \frac{π}{6})$ $y=sin(x+pi/6)$ ?

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Answer 1 · 2017-12-03T11:45:27

See below.

Explanation:

If we look at a trig function in the form:

$y = a sin (b x + c) + d$ $y =asin(bx+c)+d$

Amplitude is $888 a$ $color(white)(888) color(blue)(a)$

Period is $888 \frac{2 π}{b}$ $color(white)(888)color(blue)((2pi)/b)$

Phase shift is $888 \frac{- c}{b}$ $color(white)(888) color(blue)((-c)/b)$

Vertical shift is $888 d$ $color(white)(888)color(blue)(d)$

From: $y = sin (x + \frac{π}{6})$ $y=sin(x+pi/6)$

We can see amplitude is 1. This is the same as for $y = sin (x)$ $y=sin(x)$

The period is: $\frac{2 π}{1} = 2 π$ $(2pi)/1=2pi$ . This is the same as $y = sin x$ $y=sinx$

Phase shift is: $\frac{- \frac{π}{6}}{1} = - \frac{π}{6}$ $(-pi/6)/1=-pi/6$ This translates the graph of

$y = sin x$ $y=sinx$ $88 \frac{π}{6}$ $color(white)(88) pi/6$ units to the left.

From the above, we conclude that the graph of $y = sin (x + \frac{π}{6})$ $y=sin(x+pi/6)$ is the graph of $y = sin x$ $y=sinx$ translated $\frac{π}{6}$ $pi/6$ units to the left.

Graph of $y = sin (x + \frac{π}{6})$ $y=sin(x+pi/6)$ and $y = sin x$ $y=sinx$ on the same axes:

enter image source here

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How do you use transformation to graph the sin function and determine the amplitude and period of $y = sin (x + \frac{π}{6})$ $y=sin(x+pi/6)$ ?

1 Answer

Explanation:

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How do you use transformation to graph the sin function and determine the amplitude and period of y=sin(x+π6)y=sin(x+pi/6)?

1 Answer

Explanation:

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How do you use transformation to graph the sin function and determine the amplitude and period of $y = sin (x + \frac{π}{6})$ $y=sin(x+pi/6)$ ?