1. Lesson 2

1.4. Discover

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

 

Discover

 

You have practised graphing and finding the equation of horizontal lines. You will now learn how to graph sinusoidal functions.

 

Try This 1

 

When graphed, the function y = sin x displays an interesting pattern. In this activity you will use a table of values to graph this function.

 

tip

This is a picture of a graphing calculator.

Hemera/Thinkstock

Most scientific and graphing calculators operate in at least two angle modes: degrees and radians. When using the sin, cos, tan, sin−1, cos−1, or tan−1 functions on your calculator, you need to pay attention to the mode that the calculator is in. If the angle is in degrees, make sure the calculator is in degree mode. If the angle is in radians, make sure the calculator is in radian mode. You may need to consult your calculator’s manual or check with your teacher if you are not sure what mode your calculator is in. Your calculator should be in degree mode for Try This 1. As a quick check, sin 45° = 0.707… and sin 45 rad = 0.8509….



  1. Use a calculator to complete the following table.

    x y = sin x
    0°

    0
    30°

    0.5
    60°

    0.866
    90°

    1
    120°

     
    150°

     
    180°

     
    210°

    –0.5
    240°

     
    270°

    −1
    300°

     
    330°

     
    360°

     
    390°

     
    420°

     
    450°

     
    480°

     
    510°

    0.5
    540°

    0

    1. What patterns do you notice in the table?
    2. Using the patterns, predict the values of sin 570°, sin 600°, sin 630°, sin 660°, sin 690°, and sin 720°.

  3. Go to Plotting Template and print a copy. Use the table to graph the function y = sin x to 720° on the template.

    1. Describe the shape of the graph.
    2. What is the maximum value of the graph?
    3. What is the minimum value?
    4. Where does the graph start to repeat itself?
    5. How do you expect the graph would look if it also included larger angles?
course folder Save your responses in your course folder.