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Sec 2.1 Trigonometric Functions of Acute Angles

Sec 2.1 Trigonometric Functions of Acute Angles. October 1, 2012. Warm – Up (10/1). Right Triangle w/ Respect to Angle A. B. (x,y). hypotenuse. r. y (opposite side). A. C. x (adjacent side). Right Triangle Based Definitions of Trigonometric Functions.

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Sec 2.1 Trigonometric Functions of Acute Angles

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

  2. Warm – Up (10/1)

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

  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. 52 46 A 22

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

  9. Cofunctions B Conclusions: c a C A b

  10. Reviewing Facts about Right Triangle • 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° = ____.

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

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

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

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

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

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

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

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

  39. Function Values of Special Angles

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

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

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

  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

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