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

Question

1600 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-03T11:45:27

See below.

If we look at a trig function in the form:

$y =asin(bx+c)+d$

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

Period is $color(white)(888)color(blue)((2pi)/b)$

Phase shift is $color(white)(888) color(blue)((-c)/b)$

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

From: $y=sin(x+pi/6)$

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

The period is: $(2pi)/1=2pi$ . This is the same as $y=sinx$

Phase shift is: $(-pi/6)/1=-pi/6$ This translates the graph of

$y=sinx$ $color(white)(88) pi/6$ units to the left.

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

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

enter image source here

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