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

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Presentation transcript:

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Objective: 6-3 Graphing Sine and Cosine Functions 18 Homework  page 363, all, even, even, all.