1. How to Teach Trig Functions Sarah Benoit

2. Planning this Lesson  Inspiration Help organize my thoughts Think about what I am wanting to teach  What is this for… Unit/Chapter? Section?

4. The Key to Trigonometry Trigonometric Functions

5. Things to Know  Definition Relationship between angles of a triangle Ratios of the sides of the triangle  How is the angle represented? Theta    Trig Names Sine  Sin  Cosine  Cos  Tangent  Tan   Reciprocal Names Cosecant  Csc  Secant  Sec  Cotangent  Cot 

6. Trig Functions  Sin  Opposite/Hypotenuse  Cos  Adjacent/Hypotenuse  Tan  Opposite/Adjacent Sin  /Cos   Helpful Hint SOHCAHTOA OppositeOpposite Hypotenuse Adjacent 

7. Reciprocals of Trig Functions  Csc  1/Sin  Hypotenuse/Opposite  Sec  1/Cos  Hypotenuse/Adjacent  Cot  1/Tan  Adjacent/Opposite Cos  /Sin  OppositeOpposite Hypotenuse Adjacent 

8. On Your Own…  5 4 3 5 3 4  Hypotenuse =  Adjacent =  Opposite =  Sin  = ?  Cos  = ?  Tan  = ?  Csc  = ?  Sec  = ?  Cot  = ?

9. Unit Circle  X Y (Cos ,Sin  ) (x,y)  /4 (Cos  /4,Sin  /4)

10. Unit Circle 0  /2  3  /2  /3  /4 4  /3  /6 3  /4 5  /6 2  /3 22 (1,0) (√3/2, 1/2) (√2/2, √2/2) (1/2, √3/2) (0,1) (-1,0) (0, -1) (-√2/2,√2/2) (-√3/2, 1/2) (-1/2, √3/2) 7  /4 7  /6 5  /4 5  /3 11  /6 (-1/2, -√3/2)(1/2, - √3/2) (-√2/2, -√2/2) (-√3/2,-1/2) (√3/2,-1/2) (√2/2,- √2/2)

11. Graph of Cos  and Sec   Things to Consider Amplitude? Period? Y-intercept? Asymptotes?  Differences? Between function and its inverse  Green Globs Green Globs ? Asymptotes Differences

13. Graph of Sin  and Csc   Things to Consider Period? Amplitude? Asymptotes?  Differences? Between function and its inverse  Green Globs Green Globs

15. Cos and Sin Wave Geometer Sketchpad

16. Graph of Tan  and Cot   Things to Consider Asymptotes?  Differences? Between function and its inverse  Green GlobsGreen Globs

18. Tangent on a Circle Geometer Sketchpad B A time C D Tan D. Bennett 3/91 Tangent Tracer

19. Now What…?  Play Green Globs Expert Mode  What type of equations should I use? Trig Functions Previous forms of equations you know

20. What if I still need help?  Ask for help  Websites http://www.drmath.com/ http://www.gomath.com/  Play Green Globs  AND…..

21. TO BECOME AN EXPERT OF TRIG FUNCTIONS