Here are the steps to find the trigonometric functions of the given special right triangle angles: 1. sin(π/6) = 1/2 The angle π/6 is one of the angles in a 30-60-90 right triangle. We know that in a 30-60-90 triangle, the ratio of the sides opposite the 30°, 60°, and 90° angles are 1:√3:2. Therefore, the ratio of the side opposite the π/6 = 30° angle to the hypotenuse is 1/2. 2. tan(π/4) = 1 The angle π/4 is one of the angles in a 45-45-90

1. 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 y
x x

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 y
π
x x

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 y
π
x x

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 y
π
x x

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 y
π
x x

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 y
π
x x

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 y
π π
x x

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 y
π π
x x

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 y
π π
x x

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 y
π π
x x

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 y
π π
x x

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 y
π π
x x

13. Day 36
2. Class Work
a) 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. 2. Class Work

15. Day 38
1. Opener
1. Sketch the following angles in the given circle:
2. Solve the following operations:

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. 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. 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. 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. 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. 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. 2. Pythagorean Investigation
Conjecture #1:
c
Pythagorean Theorem
2 2
a +b
equals the square of the
hypotenuse.
€
a
b

23. 2. Pythagorean Investigation
Conjecture #1:
c
Pythagorean Theorem
2 2
a +b =
the square of the
hypotenuse.
€ €
a
b

25. 2. Pythagorean Word Problems

26. 2. Pythagorean Word Problems
pg. 482 // #1, 2, 4 - 6

27. 2. Pythagorean Word Problems
pg. 482 // #1, 2, 4 - 6
36 -
x

28. Day
1. 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. Day
1. 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. Day
1. 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?

31. Day 39
1. 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

32. Day 39
1. Opener α
1. Find the trigonometric functions
of 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. Day 39
1. Opener α
2
1. Find the trigonometric functions
of 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. Day 39
1. Opener α
2
1. Find the trigonometric functions 3
of 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. Day 39
1. Opener α
2
1. Find the trigonometric functions 3
of 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. Day 39
1. Opener α
2
1. Find the trigonometric functions 3
of 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

37. Day 39
1. Opener α
2
1. Find the trigonometric functions 3
of 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

38. 2. Special Right Triangles
How would you find the following?:
( )
1. sin π 6 =
( )
2. tan π 4 =
( )
3. sec π 3 =

39. 2. Special Right Triangles
45°
30°
60° 45°

41. 2. 30 - 60 - 90

42. 2. 30 - 60 - 90
30°
60°

43. 2. 30 - 60 - 90
30°
60°

44. 2. 30 - 60 - 90
30°
60°
1

45. 2. 30 - 60 - 90
30°
2
60°
1

46. 2. 30 - 60 - 90
30°
2
3
€ 60°
1

47. 45°
45°

48. 2. 45 - 45 - 90
45°
45°

49. 2. 45 - 45 - 90
45°
45°

50. 2. 45 - 45 - 90
45°
45°
3

51. 2. 45 - 45 - 90
45°
3
45°
3

52. 2. 45 - 45 - 90
45°
3 2
3
€
45°
3

53. 2. 45 - 45 - 90
45°
45°
1

54. 2. 45 - 45 - 90
45°
1
45°
1

55. 2. 45 - 45 - 90
45°
1 2
€ 45°
1

56. 2. Special Right Triangles
For:
( )
1. sin π 6 =

57. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =

58. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =
2

59. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =
2
3
€

60. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =
2
3
€

61. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =
30°
2
3
€

62. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =
30°
2
3
60°
€

63. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =
30°
2
3
60°
€

64. 2. Special Right Triangles
For:
We use:
( )
1. sin π 6 =
30°
2
3
60°
€
1

65. 2. Special Right Triangles
For:
( )
2. tan π 4 =

66. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =

67. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =
1

68. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =
1 2
€

69. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =
1 2
€

70. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =
1 2
€ 45°

71. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =
45°
1 2
€ 45°

72. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =
45°
1 2
€ 45°

73. 2. Special Right Triangles
For:
We use:
( )
2. tan π 4 =
45°
1 2
€ 45°
1

74. 2. Special Right Triangles
For:
( )
3. sec π 3 =

75. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =

76. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =

77. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =
30°

78. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =
30°
60°

79. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =
30°
60°

80. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =
30°
2
60°

81. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =
30°
2
60°
1

82. 2. Special Right Triangles
For:
We use:
( )
3. sec π 3 =
30°
2
3
60°
€
1

83. 3. Classwork