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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.

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Presentation on theme: "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."— Presentation transcript:

1 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.

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

3 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.

4 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)

5 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 =

6 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)

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

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

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

10 Homework Day 1 P All

11 Write the equation of the given function

12 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.

13 Homework 8.3 Worksheet


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