Module 5: Trigonometry Applications and Identities

 

In Try This 2 you checked an identity by showing that particular values make the identity true and that the expressions on both sides of the equal sign appear to have the same graphs. This check is called a verification. A verification does not prove that an equation is an identity because it is not possible to verify a trigonometric equation for every possible value.



textbook

To see an example of a verification, read “Example 1” on pages 291 to 293 of the textbook.

 

 

 

Self-Check 1

 

textbook

  1. Complete “Your Turn” from “Example 1” on page 293 of the textbook. Answer
  2. Complete questions 1, 2, and 5 on page 296 of the textbook. Answer

In Try This 2 you saw it was possible to verify an identity both graphically and numerically. In the next section you will use identities to simplify an expression.

 

Try This 3

 

Consider the expression

  1. Determine non-permissible values for the expression.

  2. Use the reciprocal and quotient identities to simplify the expression to a single trigonometric function.
  3. Pick a permissible value of θ. Check that the original expression and the simplified expression are equal for this value.
  4. Use technology to graph both the original and simplified expressions.

course folder Save your answers in your course folder.

 

Share 3

 

With a partner or group, discuss the following questions based on your answers from Try This 3.

  1. What restrictions need to be placed on your simplified version of
  2. Why is it necessary to include these restrictions?
  3. If you write that the simplified expression equals the original expression, is this an identity? Explain.

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

Try replacing sec θ using and cot θ using
Make sure to pay attention to the values that make each ratio undefined.