Este es el keynote de la semana 3 de mi curso de Trigonometría.

1. 2. Classwork
Find the following. Do not use a calculator.
( ) ( )
1. sin π 4 + cos π 3 = ( ) ( )
6. tan π 4 cos π 6 =
( ) ( )
2. sin π 6 − cos π 4 = ( ) ( )
7. csc π 4 tan π 3 =
( ) ( )
3. sin π 2 + tan π 4 = ( ) ( )
8. sec π 6 cot π 4 =
4. cos (π ) − sin (π ) = ( )
9. 4 sin π 2 − 3tan (π ) =
( ) ( )
5. sin π 4 cos π 4 = ( ) ( )
10. 5 cos π 2 − 8sin 3π 2 =

2. Day 47
1. Opener
1. Find the following:

3. Day 47
1. Opener
1. Find the following:
sin ( 0 )

4. Day 47
1. Opener
1. Find the following:
sin ( 0 ) ( )
cos π 2

5. Day 47
1. Opener
1. Find the following:
sin ( 0 ) ( )
cos π 2 sin ( −π )

6. Day 47
1. Opener
1. Find the following:
sin ( 0 ) ( )
cos π 2 sin ( −π ) ( )
tan π 2

7. Day 47
1. Opener
1. Find the following:
sin ( 0 ) ( )
cos π 2 sin ( −π ) ( )
tan π 2

8. 2. Graphs of trigonometric functions
What do you notice about the following graphs?
y = sin(x) y = 2sin(x)

9. 2. Graphs of trigonometric functions
What do you notice about the following graphs?
y = 2sin(x) y = -2sin(x)

10. 2. Graphs of trigonometric functions
What do you notice about the following graphs?
y = 2sin(x) y = 2sin(x) + 1

11. 3. Classwork
Sketch the graph of the following functions. Find the domain and range.
1. y = 3cos x
2. y = −3sin x
3. y = 3cos x + 2
4. y = −3sin x − 2

12. Day 48
1. Opener
What is the domain and range for both y = sin(x) and y = cos(x)?

13. Day 48
1. Opener
What is the domain and range for both y = sin(x) and y = cos(x)?
Domain: R
Range: [-1, 1]

14. Day 48
1. Opener
What is the domain and range for both y = sin(x) and y = cos(x)?
Domain: R Domain: R
Range: [-1, 1] Range: [-1, 1]

25. 2. Transformations of Graphs
Remember what the difference beween, y = x2 and y = (x - 2)2 was?
y = x2

26. 2. Transformations of Graphs
Remember what the difference beween, y = x2 and y = (x - 2)2 was?
y = (x - 2)2
y = x2

27. 2. Transformations of Graphs
Remember what the difference beween, y = x2 and y = (x + 2)2 was?
y = x2

28. 2. Transformations of Graphs
Remember what the difference beween, y = x2 and y = (x + 2)2 was?
y = (x + 2)2
y = x2

29. 2. Transformations of Graphs
( )
What is the graph of y = sin x − π 2 , using the graph of y = sin(x)?

30. 2. Transformations of Graphs
( )
What is the graph of y = sin x − π 2 , using the graph of y = sin(x)?

31. 2. Transformations of Graphs
What is the graph of y = cos ( x + π ) , using the graph of y = cos(x)?

32. 2. Transformations of Graphs
What is the graph of y = cos ( x + π ) , using the graph of y = cos(x)?

33. 3. Classwork
Sketch the graph of the following functions. Find the domain and range.
(
1. y = 2sin x − π 2 )
2. y = 3cos ( x − π )
3. y = − cos ( x + π )
4. y = − cos ( x + π ) + 2

34. 4. Solutions
1.

35. 4. Solutions
2.

36. 4. Solutions
3.

37. 4. Solutions
4.

38. Day 49
π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

39. Day 49
π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π sin π = 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

40. Day 49
π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π sin π = 0 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

41. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

42. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π cos 5π 3 = 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

43. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π cos 5π 3 = 1 2 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

44. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

45. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π cot 2π = 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

46. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π cot 2π = Undefined 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

47. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
(-1, 0) (1, 0)
π 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

48. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
Angle whose sine is
(-1, 0) (1, 0)
π 2π
x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

49. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
Angle whose sine is
(-1, 0) (1, 0)
π 3 2π
2 x
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

50. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
Angle whose sine is
(-1, 0) (1, 0)
π 3 2π
2 x
π
3
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

51. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
Angle whose sine is
(-1, 0) (1, 0)
π 3 2π
2 x
π or
3
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

52. π
1. Opener 2
y π
2π ⎛ − 1 , 3 ⎞ (0, 1)
⎛ 1 , 3 ⎞
3 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 3
3π ⎛ − 2 , 2 ⎞ ⎛ 2 , 2 ⎞ π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
5π ⎛ − 3 , 1 ⎞ ⎛ 3 , 1 ⎞ π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
Angle whose sine is
(-1, 0) (1, 0)
π 3 2π
2 x
π or 2π
3 3
7π ⎛ − 3 , − 1 ⎞ ⎛ 3 , − 1 ⎞ 11π
6 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 6
5π ⎛ − 2 , − 2 ⎞ ⎛ 2 , − 2 ⎞ 7π
4 ⎝ 2 2 ⎠ ⎝ 2 2 ⎠ 4
4π ⎛ − 1 2 , − 3 2 ⎞ ⎛ 1 , − 3 ⎞ 5π
3 ⎝ ⎠ 3π (0, -1) ⎝ 2 2 ⎠ 3
2

53. 2. Amplitude and Period - Definitions
The period is the time it takes the function to go through one cycle
and then start over again.
The amplitude of a periodic function y = f (x) is defined to be one
half the distance between its maximum value and its minimum value.
Amplitude is always a positive quantity.

54. 2. Amplitude and Period
y = sin(x)

55. 2. Amplitude and Period
y = sin(x)

56. 2. Amplitude and Period
y = sin(x)

57. 2. Amplitude and Period
y = sin(x)

58. 2. Amplitude and Period
y = sin(x)

59. 2. Amplitude and Period
y = sin(x)
Amplitude: 1

60. 2. Amplitude and Period
y = sin(x)
Amplitude: 1

61. 2. Amplitude and Period
y = sin(x)
Amplitude: 1 Period: 2*pi

62. 2. Amplitude and Period
y = sin(x)

63. 2. Amplitude and Period
y = sin(x)

64. 2. Amplitude and Period
y = sin(x)

65. 2. Amplitude and Period
y = sin(x)

66. 2. Amplitude and Period
y = sin(x)

67. 2. Amplitude and Period
y = sin(x)

68. 2. Amplitude and Period
y = sin(x)
Amplitude: 1

69. 2. Amplitude and Period
y = sin(x)
Amplitude: 1

70. 2. Amplitude and Period
y = sin(x)
Amplitude: 1 Period: 2*pi

71. 2. Amplitude and Period
y = 3cosx

72. 2. Amplitude and Period
y = 3cosx

73. 2. Amplitude and Period
y = 3cosx
Amplitude: 3

74. 2. Amplitude and Period
y = 3cosx
Amplitude: 3

75. 2. Amplitude and Period
y = 3cosx
Amplitude: 3
Period: 2*pi

76. 2. Amplitude and Period
y = 3sin2x

77. 2. Amplitude and Period
y = 3sin2x

78. 2. Amplitude and Period
y = 3sin2x
Amplitude: 3

79. 2. Amplitude and Period
y = 3sin2x
Amplitude: 3

80. 2. Amplitude and Period
y = 3sin2x
Amplitude: 3
Period: pi

81. 2. Amplitude and Period
1
y = 2sin x
2

82. 2. Amplitude and Period
1
y = 2sin x
2

83. 2. Amplitude and Period
1
y = 2sin x
2
Amplitude: 2

84. 2. Amplitude and Period
1
y = 2sin x
2
Amplitude: 2

85. 2. Amplitude and Period
1
y = 2sin x
2
Amplitude: 2 Period: 4*pi

86. 2. Amplitude and Period
y = -2sin3x

87. 2. Amplitude and Period
y = -2sin3x

88. 2. Amplitude and Period
y = -2sin3x
Amplitude: 2

89. 2. Amplitude and Period
y = -2sin3x
Amplitude: 2

90. 2. Amplitude and Period
y = -2sin3x
Amplitude: 2 Period: (2/3)pi

91. 2. Amplitude and Period
y = 4 cos π x

92. 2. Amplitude and Period
y = 4 cos π x

93. 2. Amplitude and Period
y = 4 cos π x
Amplitude: 4

94. 2. Amplitude and Period
y = 4 cos π x
Amplitude: 4

95. 2. Amplitude and Period
y = 4 cos π x
Amplitude: 4 Period: 2

96. 2. Amplitude and Period
y = 2sinx + 3

97. 2. Amplitude and Period
y = 2sinx + 3

98. 2. Amplitude and Period
y = 2sinx + 3
Amplitude: 2

99. 2. Amplitude and Period
y = 2sinx + 3
Amplitude: 2

100. 2. Amplitude and Period
y = 2sinx + 3
Amplitude: 2 Period: 2*pi

101. 3. Example
Sketch the graph of ( )
f (x) = 3sin x − π 4 − 1

102. 3. Example
Sketch the graph of ( )
f (x) = 3sin x − π 4 − 1

103. Day 50
1. Quiz 6