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1. Graphing secx,cscx
2. A review of reciprocals As a number increases what happens to its reciprocal? decreases
As a number decreases what happens to its reciprocal? increases
3. Chart of values for y = sinx
4. A look at y = sin x
5. Now let’s look at y = sin x and its effect on y = csc x Graphing y = csc x is easiest if you first look at y = sin x.
Notice that as sin x increases csc x will decrease and as sin x decreases csc x will increase.
When sin x = 0 then its reciprocal csc x will be undefined.
This will mean that at those 3 locations where sinx = 0 csc x will have a vertical asymptote.
6. Now let’s look at y = sin x and its effect on y = csc x When sin x is at its maximum value
csc x will be at its minimum value.
When sin x is at its minimum value
csc x will be at its maximum value.
sin x and csc x will have the same period.
7. Graphing y = csc x
9. Try this one
10. First sketch the graph of Amp = 2
Period = 2p
Phase shift: x = -p/4
11. Set up the chart for the 5 special pts.
12. Sketch sine function
13. Graphing cosecant
14. Graphing cosecant
15. Now to graph secant Remember that
Sec x = 1/cos x.
Our use of reciprocals will still come into play.
When cos x = 0 sec x will have vertical asymptotes.
When cos x is at a maximum, sec x will be at a minimum.
When cos x is at a minimum, sec x will be at a maximum.
16. Graph y = sec x
17. Graph y = sec x
