1. More Trigonometric Graphs 5.4
Essential Question: How are secant and cosecant graphs related to sine and cosine graphs?

2. Tangent and Cotangent Graph Properties
Period:
Asymptotes:
Cotangent
Period:
Asymptotes:

3. Graphing Tangent and Cotangent functions:
Find the amplitude, period, left asymptote, and right asymptote.
Make an x-y chart:
1st x-coordinate: use the left asymptote.
5th x-coordinate: use the right asymptote.
3rd x-coordinate: find the midpoint of the 1st and 5th coordinates.
2nd x-coordinate: find the midpoint of the 1st and 3rd coordinates.
4th x-coordinate: find the midpoint of the 5th and 3rd corrdinates.

4. Graphing Cont’d
Substitute the x-coordinates into the original function to find y.
Draw the asymptotes.
Plot the points in a coordinate plane.
Connect the dots with a smooth curve.

5. Examples: Graph the following functions

6. Graphing Cosecant and Secant
Graph the sine or cosine function first.
Draw asymptotes. (Hint: there will be an asymptote anywhere the sine or cosine function crosses the x-axis.)
Interchange “hills” and “valleys”. A “hill” on sine or cosine will become a “valley” on cosecant or secant. A “valley” on sine or cosine will become a “hill” on cosecant or secant.

7. Graph of Cosecant

8. Graph of Secant

9. Examples: Graph the following functions.