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Translations of sine and cosine graphs The graph will be shifted to the right by c. The graph will be shifted up d. We already know what A and B are used for.

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Identify the period, amplitude and translation: 1. 2. 3. Amp: Per: Trans: Amp: Per: Trans: Amp: Per: Trans:

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Step by Step Graphing of a Sine or Cosine function: Example: Step 1: Draw the center line of the graph by graphing the horizontal line y = d. This is also called the axis of the wave.

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Step 2: Using A, draw two horizontal lines, Y=d+a Y=d-a This gives us our maximum and minimum values for the functions (Top and bottom of the graph)

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Step 3: Determine the period of the function using B, and use this to find the new spacing of the graph. We have done this before! Period =

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Step 4 your starting point for the graph: Sin and Cos will vary: Sin –Plot the point (c,d) Cos –Plot the point (c, max)

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Graphing with translations: Graph for discussion Amp: Per: Trans:

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Graphing with translations: Graph for discussion Amp: Per: Trans:

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Graphing with translations: Graph for discussion Amp: Per: Trans:

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Homework Day 1 P. 313 9-14 All

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Write the equation of the given function

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Application At a certain spot the water level is 6m at low tide and 14 m at high tide. If the tide has period of 12.4 hours, find an equation for the water level.

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Homework 8.3 Worksheet

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