1. Lesson 2

1.9. Explore 5

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

 

So far, you have determined characteristics of a sinusoidal function from a graph. Sometimes, it is also useful to sketch a graph from given information. In the following activity, you will explore strategies to sketch sinusoidal functions.

 

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  1. Draw at least two cycles of a sinusoidal function with the following characteristics. Click on the hint buttons if you require help.

    Period

    12 rad
    Midline

    y = −1
    Maximum

    2
    Passes Through the Point

    (0, −4)

    Graph Size

     

    Midline

     

    Sketching the Graph

  2. Describe the set of steps you used to sketch the function in question 1. Will these steps work for any sinusoidal function?

course folder Save your responses in your course folder.

 

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With a partner or group, compare your strategies for sketching a sinusoidal function.

 

course folder If required, save a record of your discussion in your course folder.

The spacing between a maximum or minimum and an intersection with the midline is always  of a period. Use these key points to sketch your graph.

 

This diagram shows one period of two sinusoidal functions split at their minima, maxima, and intersection with the midline. Each segment covers a quarter period.

Next, draw the midline using the equation given in the table.
Start by determining the size of graph you will need. Think about the minimum and maximum values as well as the period.