LESSON FOUR: Graphing y  sin kx and y  coskx
The value “k” stretches or compresses the graph of y=sinx or y=cosx in the horizontal direction.
This is not as easy as stretching/compressing in the vertical direction. We can’t just multiply/divide the
x-values. The following method makes it a LITTLE easier.
1.
Recall that there are FIVE key points.
2.
Determine the period. That is, the length of one cycle (one hill and one valley). The formula for
the period is period 
3.
360
.
k
Starting at zero, make an endpoint on the right for when one cycle ends (the length of the period
you just calculated).
4.
Divide this length into FOUR equal parts and mark these points on your grid.
5.
Graph the key points on these four points.
DONE!
Example: Graph y  sin x and y  sin( 2 x) on the same grid.
1 
x .
2 
Example: Graph y  cos x and y  cos
1 
3 
Example: Graph y  sin x and y  sin  x  .