Topic 11 Periodic and Exponential Functions I

1. Topic 11Periodic and Exponential Functions I

2. Recall • A S T C

3. opp hyp + + sinθ= = = + cosθ= = = + tanθ= = = + adj hyp + + θ opp adj + +

4. opp hyp + + sinθ= = = + cosθ= = = - tanθ= = = - adj hyp - + θ opp adj + -

5. opp hyp - + sinθ= = = - cosθ= = = - tanθ= = = + adj hyp - + θ opp adj - -

6. opp hyp - + sinθ= = = - cosθ= = = + tanθ= = = - adj hyp + + θ opp adj - +

7. A S T C ll tations o entral SIN + ALL + TAN + COS +

8. A S T C ll aints each lasses SIN + ALL + TAN + COS +

9. A S T C ll heilas alk onstantly Yappity yappity… Blah blah blah !!!! SIN + ALL + TAN + COS +

10. Sine of any angle Cosine of any angle Tangent of any angle

11. Recall • A S T C • tan  = sin  / cos  • sin (90-) = cos  • cos (90-) = sin  • sin2 + cos2 =1 • sin, cos and tan of 30o , 60o and 45o

12. 30 60 sin 30o = ½ cos 30o = tan 30o = sin 60o = cos 60o = ½ tan 60o =

13. 45 45 sin 45o = cos 45o = tan 45o = 1

15. So we can express every trig ratio in terms of sin and cos

16. Model: Evaluate (a) cosec /4 (b) cot 5/3

17. Model: If sec  = 5/4, find cot  if  is acute 5 4 3

18. Model: Prove(a) cosec2x = sec x cosec x cot x(b) 1/(cosec x + 1) + 1/(cosec x -1) = 2tan x sec x

19. Model: Prove(a) cosec2x = sec x cosec x cot x(b) 1/(cosec x + 1) + 1/(cosec x -1) = 2tan x sec x