Module 4: Foundations of Trigonometry

 

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Try This 1

 

This is a photo of two cylindrical cans. One is upright and the other is on its side.

iStockphoto/Thinkstock

You want to unwrap some information about the circumference of a tin can. You don’t want to cut the can, so you need to think of another way to unwrap the information. How does the circumference of a tin can relate to radian measures in a circle?


 

textbook

  1. Complete “Investigate Circular Number Lines” parts 1 to 7 on pages 180 and 181 of the textbook. Watch Investigate Circular Number Lines to see the steps explained.

     
    This is a play button that opens Investigate Circular Number Lines.
  2. Since each number line shows the circumference of the can and the circle to be 2π units, what assumption is being made about the length of the radius?1
  3.  
    1. Determine the coordinates for . Start by marking the coordinates for all the points on the circle that are midway between the axes.

       
      This diagram shows a circle divided into 8ths with the centre marked O. The horizontal division on the right side is labelled P at zero equals 1, 0. The first division counterclockwise from this point is labelled pi divided by 4.
      Adapted from Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.
    2. What is the only difference in the coordinates for these four points that are midway between the axes?

course folder Save your responses in your course folder.

 

Share 1

 

With a partner or in a group, compare your responses from Try This 1 questions 2 and 3 and the methods you used to determine the coordinates for the eight points.

 

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

 

1 Source: Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.

Draw a vertical line from point P to the horizontal axis. Use properties of the 45°-45°-90° triangle that you already know to determine the lengths of the sides of the triangle.