As c changes...

In all previous examples, the value of c has been 0. How does changing the value of c affect the sine curve? Once again, let's explore with several examples:

 

When c=0, the graph of y=sin x passes through ..., x=-, x=-, the origin, x=, x=,.... For the graph of y=sin(x+1), c=1. This curve passes through the following points: ..., x=--1, x=--1, x=-1, x=-1, x=-1,.... The graph has been shifted or translated to the left by -1 units along the x-axis.

In general, the graph of y=sin (x+c) translates to the left on the x-axis by c units, if c is positive.

Now, let's consider what happens when c is negative. From our example y=sin(x-2), we can name the points where the curve crosses the x-axis. These are: ..., x=-+2, x=-+2, x=2, x=+2, x=+2,.... So, the graph appears to be shifted to the right along the x-axis by 2 units.

In general, if c is negative, the graph of y=sin (x+c) translates to the right along the x-axis by a distance of units.


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