1. Chapter 5 – Trigonometric Functions: Unit Circle Approach 5.4 - More Trigonometric Graphs

2. Cosecant

3. Graphing y = Acsc(Bx - C) +D Graph the sine function with dotted lines. The max point of the sine function is the MINIMUM point of the cosecant function. The min point of the sine function is the MAXIMUM point of the cosecant function. Where the sine function and y = D intersect are the vertical asymptotes of the cosecant function.

4. Cosecant Example Graph the following equation:

5. Secant

6. Graphing y = Asec(Bx - C) + D Graph the cosine function with dotted lines. The max point of the cosine function is the MINIMUM point of the secant function. The min point of the cosine function is the MAXIMUM point of the secant function. Where the cosine function and y = D intersect are the vertical asymptotes of the secant function.

7. Secant Example Graph the following equation:

8. Tangent

9. Graphing y = Atan(Bx - C) + D Find two consecutive asymptotes A pair of consecutive asymptotes occur at Find the point midway between the asymptotes (this is the x-intercept if there is no vertical shift; the y-value is the D). Find the points on the graph that are ¼ and ¾ of the way between the asymptotes. These points will have the y-values of D+A and D-A respectively.

10. Tangent Example Graph the following equation:

11. Cotangent

12. Graphing y = Acot(Bx - C) + D Find two consecutive asymptotes A pair of consecutive asymptotes occur at Find the point midway between the asymptotes (this is the x-intercept if there is no vertical shift; the y-value is the D). Find the points on the graph that are ¼ and ¾ of the way between the asymptotes. These points will have the y-values of –A+ D and A+D respectively.

13. Cotangent Example Graph the following equation:

14. Graphing Summary