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Understanding Sinusoidal Graphs: Phase Shift and General Sine & Cosine Curves

In this lesson, we explore the characteristics of sinusoidal graphs, including phase shifts in general sine and cosine curves. We start by graphing given equations and verifying the period, amplitude, and shifts. Specific examples are provided to illustrate the concept, such as checking key points on the graph. Homework exercises reinforce learning with practical problems to further develop your understanding of sinusoidal functions. Gain confidence in recognizing and graphing periodic functions through systematic approaches.

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Understanding Sinusoidal Graphs: Phase Shift and General Sine & Cosine Curves

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  1. 7.8 (Day 2) Sinusoidal Graphs with Phase Shift

  2. General Sine & Cosine Curves first point of graph

  3. Ex 1) Graph Check Period: b c a d = 1 = = 1 = 0 1 –1 Per = 2𝝅 IL: Check a point: (easier to match c)

  4. Ex 2) Graph Factor out b Check Period: b c a d = 3 = = = 0 Per = IL: Check a point:

  5. Ex 3) Graph Factor out b Check Period: b c a d = = = 4 = –2 4 2 –2 Per = IL: –4 –6 Check a point:

  6. Homework #721 Pg. 452 5 – 11 odd, 29 – 35 odd Add ‘d’ values: #29: + 1 #31: – 1 #33: + 2 #35: – 2

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