Graphing y=sin(kx) and y=cos(kx)
By the end of this lesson students will be able to:
• graph y=sin(kx) and y=cos(kx) for various values of k.
• describe y=sin(kx) and y=cos(kx) in terms of horizontal stretches or compressions
• determine the period of a trigonometric function when given the equation
• graph y=asin(k(x­d))+c and y=acos(k(x­d))+c Investigate the effect of changing the value of k.
Make a table of values and graph y=sin(2x)
x
0
30
45
60
90
120 135 150 180 2x
sin(2x)
Make a table of values and graph x
0
30
45
60
90
120 135 150 180 2x
In the equation y=sin(kx) and y=cos(kx)
If |k|>1, then there is a horizontal compression of 1/k units; the period becomes smaller; the period will be 360/k
For example in y=sin(2x), there is a horizontal compression of y=sin(x) by a factor of 1/2 and the period is 360/2=180 degrees.
To graph this function, divide all of the horizontal distances on y=sin(x) by 2. (Hint ­ use the 5 points)
In the equation y=sin(kx) and y=cos(kx)
If |k|<1, then there is a horizontal stretch of 1/k units; the period becomes bigger; the period will be 360/k
For example in y=sin(1/2x), there is a horizontal stretch of y=sin(x) by a factor of 2 and the period is 360/(1/2)=720 degrees.
To graph this function, multiply all of the horizontal distances on y=sin(x) by 2. (Hint ­ use the 5 points)
In the equation y=sin(kx) and y=cos(kx)
If k<0, then there is a horizontal reflection of the graph of y=sin(x) about the y­axis.
Note that y=sin(­x) is different than y=sin(­x), but
y=cos(­x) is the same as y=cos(x). Why?
Note that a negative has to factored out if there is a combination of a horizontal reflection and a horizontal translation and it is not already factored.
Eg.
y=sin(­x+60)
Factor
y=sin(­(x­60))
You Try
Graph: a) y=sin(3x)
You Try
Graph: b)
Putting it all together.
Graph for Homework
Pages 309