1. way more fun the sine and cosine
CscΘ and SecΘ Graphs
way more fun the sine and cosine

2. CscΘ??? How can we find cscΘ?
Use your table of values to plot the cscΘ function.

3. Looking at the Sine Graph
Look at your worksheet from last week for sine’s key points

4. What we know about csc
Cscϴ = 1/sinϴ

5. Use sine values to get the following:
csc(0°) = ____0_____ csc(45°) = _2/√2 =√2 csc(90°) = ___1___ csc(135°) = _2/√2 =√2
csc(180°) = undefined csc(270°) = ___-1___ csc(360°) = undefined
csc(1°) = ____57.3_ csc(179°) = 57.3
csc(181°) = __-57.3_ csc(359°) = __-57.3_

6. In general: asymptotes = 180°n Every 180 degrees
Where do they go?
What do they mean?
0°180°360°
In general: asymptotes = 180°n
Every 180 degrees
Where the graph cannot occur. There are no outputs at those points.

7. Use the graph and what you know about the sine graph to complete the following:
Period: 360 or 2π
With transformations:360/b or 2π/b
Vertical Asymptotes: x = nπ = n180°
Maximums: (270, -1) -Where minimums were
Minimums: (90,1) - Where maximums were
Where sine or cosine was 0
At multiples of 180°

8. Let’s see it Csc Graph Sine and Csc Graphs
Make sure to click on the links in pale blue above (there are two) – use the sliders to adjust the values and see how the transformations and translations affect the parent graphs

9. To graph cosecant graphs:
First graph the sine graph with the transformations (just as we did in the last section).
Put asymptotes where the sine graph was zero
Put maximums where the sine graph had minimums
Put minimums where the sine graph had maximums

10. Examples
Try the example on the back of the first page at this time – graph the sine and cosine graphs and go from there!

11. SecΘ???? How can we find secΘ?
Use your table of values to plot the secΘ function.

12. Looking at the Cosine Graph
Cosine Key Points: ( , ), ( , ), ( , ), ( , ), ( , )

13. What we know about sec
secϴ = 1/cosϴ

14. No output value at those x-values At x = 90 + 180n At x = π/2 +πn
Asymptotes
Where are they?
What do they mean?
No output value at those x-values
At x = n
At x = π/2 +πn
Starting at 90 and every 180 after that

15. Let’s See It
Make sure to click on the links in pale blue below(there are two) – use the sliders to adjust the values and see how the transformations and translations affect the parent graphs
secant

16. To graph secant graphs:
First graph the cosine graph with the transformations (just as we did in the last section).
Put asymptotes where the cosine graph was zero
Put maximums where the cosine graph had minimums
Put minimums where the cosine graph had maximums

17. Examples
Try the example on the back of the first page at this time – graph the sine and cosine graphs and go from there!