Module 4: Foundations of Trigonometry

 

You have looked at how the parameters c and d can be used to sketch the graph of a sine or cosine function. In Try This 2 you will see how this process can also be done in reverse by determining c and d from a given graph.

 
Try This 2
  1. Determine the value of the midline for the graph shown. Use this value to determine d in the equation y = sin(x − c) + d.

     
    A graph shows a sinusoidal function. The y-intercept is at negative 2, the length of a cycle is 2 pi, the minimum value is negative 3, and the maximum value is negative 1. The graph is sloped downwards at the y-intercept.
  2. Determine a value on the midline where the graph is increasing. Use this value to determine c in the equation y = sin(x − c) + d.

course folder Save a copy of your responses in your course folder.

 
Share 2

 

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

  1. How many possible c-values are there for the graph?  If there’s more than one value, give a second value and explain.
  2. How many possible d-values are there for the graph?  If there’s more than one value, give a second value and explain.
  3. How would your method for determining c be different if this were a cosine graph?

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