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Week 8 - Trigonometry

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• I cut the word problem assignment waaay back. Painful.\n
• I cut the word problem assignment waaay back. Painful.\n
• I cut the word problem assignment waaay back. Painful.\n
• Q. The animation here shows the path of the fly to the spider and then the right triangle. Do easier problems for the treasure hunt.\n
• Q. The animation here shows the path of the fly to the spider and then the right triangle. Do easier problems for the treasure hunt.\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Why are they special?\n
• The 30-60-90 is one half the equilateral triangle.\n
• The 30-60-90 is one half the equilateral triangle.\n
• The 30-60-90 is one half the equilateral triangle.\n
• The 30-60-90 is one half the equilateral triangle.\n
• The 30-60-90 is one half the equilateral triangle.\n
• The 30-60-90 is one half the equilateral triangle.\n
• The 45-45-90 is one half a square.\n
• The 45-45-90 is one half a square.\n
• The 45-45-90 is one half a square.\n
• The 45-45-90 is one half a square.\n
• The 45-45-90 is one half a square.\n
• Again we&amp;#x2019;re Pythagorizing, but looking for a rule, a pattern.\n
• Again we&amp;#x2019;re Pythagorizing, but looking for a rule, a pattern.\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).\n
• Week 8 - Trigonometry

1. 1. Day 361. Openera) Draw a XY plane.b) Draw a circle with its center at the origin.c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y y x x
2. 2. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ x x
3. 3. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ x x
4. 4. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ x x
5. 5. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ x x
6. 6. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ x x
7. 7. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ π x x
8. 8. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ π x x
9. 9. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ π x x
10. 10. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ π x x
11. 11. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ π x x
12. 12. Day 36 1. Opener a) Draw a XY plane. b) Draw a circle with its center at the origin. c) Draw the following angles, in standard position: θ = 3 2π θ = 5 3π y yπ π x x
13. 13. Day 362. Class Worka) Find someone to work with.b) You’ll be working in pairs.c) Sketch the given angles in a plane like the one below.
14. 14. 2. Class Work
15. 15. Day 381. Opener 1. Sketch the following angles in the given circle: 2. Solve the following operations:
16. 16. Conjecture #1: hypotenuse Pythagorean Theorem The sum of the squares of the legs of a right triangle equals the square of the hypotenuse.legs
17. 17. 2. Pythagorean Investigation Conjecture #1: hypotenuse Pythagorean Theorem The sum of the squares of the legs of a right triangle equals the square of the hypotenuse.legs
18. 18. 2. Pythagorean Investigation Conjecture #1: hypotenuse Pythagorean Theorem The sum of the squares of the legs of a right triangle equals the square of the hypotenuse.legs
19. 19. 2. Pythagorean Investigation Conjecture #1: hypotenuse Pythagorean Theorem The sum of the squares of the legs of a right triangle equals the square of the hypotenuse.legs
20. 20. 2. Pythagorean Investigation Conjecture #1: c Pythagorean Theorem The sum of the squares of the legs of a right triangle equals the square of the hypotenuse.a b
21. 21. 2. Pythagorean Investigation the law of cosines change this to c2 = a2 + b2 in anticipation of Conjecture #1: c Pythagorean Theorem The sum of the squares of the legs of a right triangle equals the square of the hypotenuse.a b
22. 22. 2. Pythagorean Investigation Conjecture #1: c Pythagorean Theorem 2 2 a +b equals the square of the hypotenuse. €a b
23. 23. 2. Pythagorean Investigation Conjecture #1: c Pythagorean Theorem 2 2 a +b = the square of the hypotenuse. € €a b
24. 24. 2. Pythagorean Word Problems
25. 25. 2. Pythagorean Word Problems pg. 482 // #1, 2, 4 - 6
26. 26. 2. Pythagorean Word Problems pg. 482 // #1, 2, 4 - 6 36 - x
27. 27. Day1. Opener A spider and a fly are at opposite corners of a rectangular room that measures 14 ft. x 7 ft. x 10 ft. a) What is the distance between them? b) What is the shortest path the spider could take to eat the fly? 10 ft. 7 ft. 14 ft. c) What is the only letter that doesn’t appear in a U.S. state?
28. 28. Day1. Opener A spider and a fly are at opposite corners of a rectangular room that measures 14 ft. x 7 ft. x 10 ft. a) What is the distance between them? b) What is the shortest path the spider could take to eat the fly? 10 ft. 7 ft. 14 ft. c) What is the only letter that doesn’t appear in a U.S. state?
29. 29. Day1. Opener A spider and a fly are at opposite corners of a rectangular room that measures 14 ft. x 7 ft. x 10 ft. a) What is the distance between them? b) What is the shortest path the spider could take to eat the fly? 10 ft. 7 ft. 14 ft. c) What is the only letter that doesn’t appear in a U.S. state?
30. 30. Day 391. Opener a) A 25 foot ladder leans against a wall. It touches the wall 24 feet off the ground. If you slide the base of the ladder back 10 feet on the ground, how far does it slide down the wall? b) A pyramid has a base apothem of 8 ft. and a base side length of 12 ft. The triangles that make up its side each have height 40 ft. It’s total surface area is 7200 sq ft. How many edges does the pyramid have? c) What do you call someone from: Louisiana, Maine, Connecticut, New Jersey, Massachusetts
31. 31. Day 391. Opener α 1. Find the trigonometric functionsof the angle α andβ if: β 2.Solve the following equations: a) 5 x−2 =3 3x+2 b) ln ( x + 1) + ln ( x − 2 ) = ln ( x 2 ) 3. Solve the following: 1 ⎡ 8 ⎛ 24 ⎞ ⎤ 1− −3 − ⎢ − − 50 ⎜ 1− ⎟ ⎥ b) 1− 10 ⎣ 2 ⎝ 25 ⎠ ⎦ 1 a) 1− ⎛ 1 ⎞ 1 −4 − ⎜ − 1⎟ 1− ⎝ 2 ⎠ 10
32. 32. Day 391. Opener α 2 1. Find the trigonometric functionsof the angle α andβ if: β 2.Solve the following equations: a) 5 x−2 =3 3x+2 b) ln ( x + 1) + ln ( x − 2 ) = ln ( x 2 ) 3. Solve the following: 1 ⎡ 8 ⎛ 24 ⎞ ⎤ 1− −3 − ⎢ − − 50 ⎜ 1− ⎟ ⎥ b) 1− 10 ⎣ 2 ⎝ 25 ⎠ ⎦ 1 a) 1− ⎛ 1 ⎞ 1 −4 − ⎜ − 1⎟ 1− ⎝ 2 ⎠ 10
33. 33. Day 391. Opener α 2 1. Find the trigonometric functions 3of the angle α andβ if: β € 2.Solve the following equations: a) 5 x−2 =3 3x+2 b) ln ( x + 1) + ln ( x − 2 ) = ln ( x 2 ) 3. Solve the following: 1 ⎡ 8 ⎛ 24 ⎞ ⎤ 1− −3 − ⎢ − − 50 ⎜ 1− ⎟ ⎥ b) 1− 10 ⎣ 2 ⎝ 25 ⎠ ⎦ 1 a) 1− ⎛ 1 ⎞ 1 −4 − ⎜ − 1⎟ 1− ⎝ 2 ⎠ 10
34. 34. Day 391. Opener α 2 1. Find the trigonometric functions 3of the angle α andβ if: β € 2.Solve the following equations: a) 5 x−2 =3 3x+2 b) ln ( x + 1) + ln ( x − 2 ) = ln ( x 2 ) 3. Solve the following: 1 ⎡ 8 ⎛ 24 ⎞ ⎤ 1− −3 − ⎢ − − 50 ⎜ 1− ⎟ ⎥ b) 1− 10 ⎣ 2 ⎝ 25 ⎠ ⎦ 1 a) 1− ⎛ 1 ⎞ 1 −4 − ⎜ − 1⎟ 1− ⎝ 2 ⎠ 10
35. 35. Day 391. Opener α 2 1. Find the trigonometric functions 3of the angle α andβ if: β € 2.Solve the following equations: a) 5 x−2 =3 3x+2 b) ln ( x + 1) + ln ( x − 2 ) = ln ( x 2 ) 3. Solve the following: 1 ⎡ 8 ⎛ 24 ⎞ ⎤ 1− −3 − ⎢ − − 50 ⎜ 1− ⎟ ⎥ b) 1− 10 ⎣ 2 ⎝ 25 ⎠ ⎦ 1 a) 1− ⎛ 1 ⎞ 1 −4 − ⎜ − 1⎟ 1− ⎝ 2 ⎠ 10
36. 36. Day 391. Opener α 2 1. Find the trigonometric functions 3of the angle α andβ if: β € 1 2.Solve the following equations: a) 5 x−2 =3 3x+2 b) ln ( x + 1) + ln ( x − 2 ) = ln ( x 2 ) 3. Solve the following: 1 ⎡ 8 ⎛ 24 ⎞ ⎤ 1− −3 − ⎢ − − 50 ⎜ 1− ⎟ ⎥ b) 1− 10 ⎣ 2 ⎝ 25 ⎠ ⎦ 1 a) 1− ⎛ 1 ⎞ 1 −4 − ⎜ − 1⎟ 1− ⎝ 2 ⎠ 10
37. 37. 2. Special Right TrianglesHow would you find the following?: ( ) 1. sin π 6 = ( ) 2. tan π 4 = ( ) 3. sec π 3 =
38. 38. 2. Special Right Triangles 45° 30° 60° 45°
39. 39. 2. 30 - 60 - 90
40. 40. 2. 30 - 60 - 90 30° 60°
41. 41. 2. 30 - 60 - 90 30° 60°
42. 42. 2. 30 - 60 - 90 30° 60° 1
43. 43. 2. 30 - 60 - 90 30° 2 60° 1
44. 44. 2. 30 - 60 - 90 30° 2 3 € 60° 1
45. 45. 45° 45°
46. 46. 2. 45 - 45 - 90 45° 45°
47. 47. 2. 45 - 45 - 90 45° 45°
48. 48. 2. 45 - 45 - 90 45° 45° 3
49. 49. 2. 45 - 45 - 90 45° 3 45° 3
50. 50. 2. 45 - 45 - 90 45° 3 2 3 € 45° 3
51. 51. 2. 45 - 45 - 90 45° 45° 1
52. 52. 2. 45 - 45 - 90 45° 1 45° 1
53. 53. 2. 45 - 45 - 90 45° 1 2 € 45° 1
54. 54. 2. Special Right TrianglesFor: ( ) 1. sin π 6 =
55. 55. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 =
56. 56. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 = 2
57. 57. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 = 2 3 €
58. 58. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 = 2 3 €
59. 59. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 = 30° 2 3 €
60. 60. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 = 30° 2 3 60° €
61. 61. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 = 30° 2 3 60° €
62. 62. 2. Special Right TrianglesFor: We use: ( ) 1. sin π 6 = 30° 2 3 60° € 1
63. 63. 2. Special Right TrianglesFor: ( ) 2. tan π 4 =
64. 64. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 =
65. 65. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 = 1
66. 66. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 = 1 2 €
67. 67. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 = 1 2 €
68. 68. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 = 1 2 € 45°
69. 69. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 = 45° 1 2 € 45°
70. 70. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 = 45° 1 2 € 45°
71. 71. 2. Special Right TrianglesFor: We use: ( ) 2. tan π 4 = 45° 1 2 € 45° 1
72. 72. 2. Special Right TrianglesFor: ( ) 3. sec π 3 =
73. 73. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 =
74. 74. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 =
75. 75. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 = 30°
76. 76. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 = 30° 60°
77. 77. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 = 30° 60°
78. 78. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 = 30° 2 60°
79. 79. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 = 30° 2 60° 1
80. 80. 2. Special Right TrianglesFor: We use: ( ) 3. sec π 3 = 30° 2 3 60° € 1
81. 81. 3. Classwork