Discover

 

Try This 1

 

Take out the unit circle you made in Lesson 3: Try This 4. You were able to use this diagram to visualize angles and determine some trigonometric ratios. Another way to visualize some of the same information is to plot a graph of the y-coordinate of the intersection of the terminal arm and the unit circle, P(x, y), versus the angle θ of the terminal arm. Consider these examples:

• When θ = 0, the y-coordinate of P is 0, so the point (0, 0) is plotted. (shown as blue in diagram)
• When the y-coordinate of P is so the point is plotted. (shown as red in diagram)
  
  

Open Table and Graph Template.

1. Complete the table for all angles on the unit circle you produced in Lesson 3: Try This 4.
2. Graph the angle θ against the y-coordinate using the labelled axis provided.

Save your completed copy of Table and Graph Template in your course folder.

 

Share 1

 

With a partner or group, discuss the following questions based on your graph created in Try This 1.

1. What is the shape of the graph you produced?
2. Could you extend this pattern for angles larger than 2π? If so, predict the shape of the graph.
3. Could you extend this pattern for angles less than 0? If so, predict the shape of the graph.

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