1. Sec 2.1 Trigonometric Functions of Acute Angles October 1, 2012

2. Warm – Up (10/1)

3. B A C (x,y) y (opposite side) r x (adjacent side) hypotenuse Right Triangle w/ Respect to Angle A

4. Right Triangle Based Definitions of Trigonometric Functions For any acute angle A in standard position,

5. Right Triangle Based Definitions of Trigonometric Functions For any acute angle A in standard position,

6. I Do It Find the values of the six trigonometric functions for angle A. 14 19 23 A

7. We Do It Together Find the values of the six trigonometric functions for angle A. 46 52 22 A

8. Cofunctions Find the values of the six trigonometric functions for angle A and B. 46 52 22 A

9. Conclusions: Cofunctions B C A a b c

10. The sum of the three angles in any triangle is ____. Angle B and angle A are ____________ angles. (Since angle C = 90°, the sum of angle A + angle B = 180°- 90° = ____. Reviewing Facts about Right Triangle

11. Since angles A and B are: complementary & sinA = cosB (A + B = 90°) The functions sine and cosine are called COFUNCTIONS! Cofunctions

12. Since & sinA = cosB Thus…

13. Cofunction Identities For any acute angle A, since

14. Cofunction Identities For any acute angle A, since

15. Cofunction Identities For any acute angle A, since

16. I Do It Write the following in terms of its cofunctions.

17. We Do It Together Write the following in terms of its cofunctions.

18. You Do It Together Write the following in terms of its cofunctions.

19. Homework Pg. 68 #7, 9, 11, 13, 15,17, 19, 21

20. Warm – Up (10/2) Write the following in terms of its cofunctions.

21. Since angles A and B are: complementary & sinA = cosB (A + B = 90°) The functions sine and cosine are called COFUNCTIONS! Cofunctions

22. I Do It Find a value of θ satisfying each equation. Assume that all angles involved are acute angles.

23. We Do It Together Find a value of θ satisfying each equation. Assume that all angles involved are acute angles.

24. You Do It Together Find a value of θ satisfying each equation. Assume that all angles involved are acute angles.

25. Comparing Function Values of Special Angles r A A r A r

26. Conclusion: As A increases, y increases. Since r is fixed, sinA increases. r A y A r y A r y

27. Conclusion: As A increases, x decreases. Since r is fixed, cosA decreases. r A x A r x A r x

28. Conclusion: As A increases, y increases and x decreases. Since r is fixed, tanA increases. r A x A r y x A r x y y

29. I Do It Tell whether each statement is true or false. TRUE

30. We Do It Together Tell whether each statement is true or false. FALSE

31. You Do It Together Tell whether each statement is true or false. TRUE

32. You Do It Together Tell whether each statement is true or false. FALSE

33. Homework (10/2) Pg. 69 # 23 – 33 odds

34. Warm – Up (10/3) Tell whether each statement is true or false.

35. Trigonometric Function Values of Special Angles 30°- 60°- 90° Triangle: 30° 60°60° 1 60°60° 1 x 1 1

36. 60° 1 30° Trigonometric Function Values of 30°-60°-90° Angles For 30° angle: Hypotenuse = Side Opposite = Side Adjacent =

37. 30° 60° Trigonometric Function Values of 30°-60°-90° Angles For 60° angle: Hypotenuse = Side Opposite = Side Adjacent = 1 30°

38. Trigonometric Function Values of 45°-45°-90° Angles 45° x x 1 For 45° angle: Hypotenuse = Side Opposite = Side Adjacent =

39. Function Values of Special Angles θ sin θ cos θ tan θ cot θ sec θ csc θ 30° 45° 60°

40. I Do It Give the exact trigonometric function value.

41. We Do It Together Give the exact trigonometric function value.

42. A line makes a 30° angle with the x – axis and crosses through the origin. What is the equation of the line? We Do It Together

43. You Do It Together A line makes a 45° angle with the x – axis and crosses through the origin. What is the equation of the line?

44. We Do It Together

45. You Do It Together