Module 5: Lesson 5

 

Self-Check 3
  1. Questions 7.a., 8, 10.a., 11.a., and 13 on pages 314 and 315 of the textbook
    1.  
      1. One possible solution is shown.

         
        LS RS

        csc 2x


    2. Hanna’s method will lead to solving the proof faster. In her method the first step leads immediately to a single term in the numerator; only one other step is required to get the two sides to be identical. Chloe’s method will work, but her method will require factoring followed by further use of identities in order to get the two sides to look identical.

      Hanna’s method is shown.

       
      LS RS

      −tan x


    1.  

      1. A graphical representation may look like this.

        This is a graph of two functions that completely overlap each other, so it appears like only one function is graphed. One function is y equals cosecant x divided by two times cosine x. The second function is y equals cosecant 2 times x.


        A possible proof is as follows:

         
        LS RS

        csc 2x



    2.  
      1. One possible solution is shown.

         
        LS RS

        csc x


    1. One possible solution is shown.

       
      LS RS

      2 cos x cos y





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