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Comprehensive Guide to Sine and Cosine Functions Graphs

Explore the basics of sine and cosine graphs, equations, and properties including amplitude, period, maxima, minima, zeros, and translations. Understand the definitions and concepts to master these fundamental functions.

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Comprehensive Guide to Sine and Cosine Functions Graphs

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  1. Chapter 4: Lesson 4.5Graphs of Sine and Cosine Functions Equations of Sine and Cosine Functions

  2. Basic Sine and Cosine Graphs Amplitude =1 Period = 2π Domain: {ARN} Range: [-1, 1] y = sin x or y = 1 sin (1x - 0) + 0 Where are the maxima and minima? Where are the zeros?

  3. Amplitude =1 Period = 2π Domain: {ARN} Range: [-1, 1] y = cos x or y = 1 cos (1x - 0) + 0 Where are the maxima and minima? Where are the zeros?

  4. Definition of Amplitude of Sine and Cosine Curves Amplitude = (Stretch/Compress Vertically) #31 Graph 2 periods of f(x) = -2 sin x and g (x) = 4 sin x

  5. Vertical Translation of Sine and Cosine Curves Graph 2 periods of f(x) = sin x + 2 and g (x) = sin x - 3

  6. Definition of Period of Sine and Cosine Curves Period = (Horizontal Stretch/Compression) Graph 2 periods of f(x) = cos 3x and g (x) = cos 1/3x

  7. Definition of Horizontal Translation (Phase Shift) Phase Shift = Graph 2 periods of f(x) = and g (x) =

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