Module 5: Trigonometry Applications and Identities

 

Self-Check 3
  1. Complete the activity in “Sum and Difference Identities for Sine and Cosine.”

     
    This play button opens “Sum and Difference Identities for Sine and Cosine.”
    Screenshot reprinted with permission of ExploreLearning

 

textbook

  1. Complete questions 7, 8.b., 8.c., 10, 20.b., and 20.c. on pages 306 and 307 of the textbook. Answer


So far you have used identities to simplify expressions. Sometimes a trigonometric identity can be useful when solving an equation. Try This 4 illustrates this.

 

Try This 4


Consider the equation .

  1. Why is this equation difficult to solve algebraically in its current form?
  2. Which identity will allow you to convert cos2 x to an expression that only uses sines?
  3. Convert the equation to only sines and solve the equation for the domain 0 ≤ x < 2π.
  4. Substitute the solution you found in question 3 back into the original equation. Does the result make sense? Explain.

course folder Save your responses in your course folder.

 

Share 3

 

With a partner or group, discuss the following questions based on the information from Try This 4.

  1. Why was it necessary to rewrite the equation so it only had one trigonometric function?
  2. Why is it easier to convert cos2 x to sines than sin x to cosines for this problem?
course folder If required, save a record of your discussion in your course folder.