Module 4: Foundations of Trigonometry

 

Explore

 

In Discover you plotted the points (θ, y-coordinate of P(x, y)) where P is the intersection of the terminal arm and the unit circle. You may recall from Lesson 4 that the y-coordinate of P(x, y) corresponds to sin θ if P is on the unit circle. This means the points you plotted in Discover are (θ, sin θ) or the function y = sin θ.  A similar process can be used to produce a graph of y = cos θ. As in previous modules, y = sin θ and y = cos θ can also be represented using function notation as f(x) = sin θ and f(x) = cos θ.

 

This diagram shows the point P with coordinates cosine theta and sine theta when the terminal arm of angle theta intersects the unit circle. Arrows from the angle theta and the y-coordinate sine of theta show the coordinates corresponding to the point theta and the sine of theta on a coordinate grid.

 

Try This 2

 

Use Cosine Table and Graph Template to respond to the following questions.

  1. Fill in Cosine Table and Graph Template for y = cos θ.
  2. Graph y = cos θ using the labelled axis provided.
  3. What are the maximum and minimum values? 
  4. Half the distance between the maximum and minimum value is called the amplitude. What is the amplitude for y = cos θ?

  5. Label the y-intercept.

  6. What is the range of the graph?

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

 
Share 2

 

With a partner or group, discuss the following questions based on the graph you created in Try This 2.

  1. How is the graph of y = cos θ that you produced similar to the graph of y = sin θ from Discover? How are the graphs different?
  2. What is the amplitude of y = sin θ from Try This 1?

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

This illustration shows a sinusoidal curve. A horizontal line across the top shows the maximum values and a horizontal line across the bottom shows the minimum values. Halfway between the maximum and minimum is a median line. The distance between the median and the maximum lines is labeled the amplitude. There is an equation below the diagram that says the amplitude is equal to the maximum minus the minimum divided by two.