1. 1 What you will learn  How to graph a basic sin and cos function

2. Objective: 6-3 Graphing Sine and Cosine Functions 2 Review of Functions  A quick review of yesterday:..\..\..\Desktop\Trigonometry_UnitCircle_SixFunctions. gsp

3. Objective: 6-3 Graphing Sine and Cosine Functions 3 A Little Vocabulary  If a “function” has repeating values over an interval, the function is said to be periodic.  The interval of “repeat” is the period of the function.

4. Objective: 6-3 Graphing Sine and Cosine Functions 4 “Real World” Example Yearly temperatures in Baltimore and Asheville

5. Objective: 6-3 Graphing Sine and Cosine Functions 5 Determining If a Function is Periodic  Page 360.

6. Objective: 6-3 Graphing Sine and Cosine Functions 6 Graphing a Basic Sine Function x y Basic Values

7. Objective: 6-3 Graphing Sine and Cosine Functions 7 The Basic Sin Graph 4. The x-intercepts are located at 5. y-intercept is 0 6. Maximum values are y=1 and occur when 7. Minimum values are y = -1 and occur when Characteristics: 1. Period is. 2. Domain: all real 3. Range: all real between -1 and 1

8. Objective: 6-3 Graphing Sine and Cosine Functions 8 Determine Values from a Graph  Example: Find by referring to the graph of the sine function

9. Objective: 6-3 Graphing Sine and Cosine Functions 9 You Try  Find by referring to the graph of the sine function.

10. Objective: 6-3 Graphing Sine and Cosine Functions 10 Finding Angle Values Given the Graph  Find the values for which sin = 0 is true.

11. Objective: 6-3 Graphing Sine and Cosine Functions 11 You Try  Find the value of for which sin = -1 is true.

12. Objective: 6-3 Graphing Sine and Cosine Functions 12 Graphing on an Interval  Example: Graph y = sin x for

13. Objective: 6-3 Graphing Sine and Cosine Functions 13 You Try  Graph y = sin x for

14. Objective: 6-3 Graphing Sine and Cosine Functions 14 Graphing a Basic Cosine Function x y Basic Values

15. Objective: 6-3 Graphing Sine and Cosine Functions 15 The Basic Cos Graph 4. The x-intercepts are located at 5. y-intercept is 1 6. Maximum values are y=1 and occur when where n is an even integer 7. Minimum values are y = -1 and occur when where n is an odd integer Characteristics: 1. Period is. 2. Domain: all real 3. Range: all real between -1 and 1

16. Objective: 6-3 Graphing Sine and Cosine Functions 16 Determining What Type of Graph  Determine whether the graph represents y = sin x or y = cos x, or neither. 1

17. Objective: 6-3 Graphing Sine and Cosine Functions 17 You Try  Determine whether the graph represents y = sin x or y = cos x, or neither. 1

18. Objective: 6-3 Graphing Sine and Cosine Functions 18 Homework  page 363, 13-15 all, 20-30 even, 32-36 even, 37- 39 all.