Module 5: Lesson 3

 

Self-Check 1
  1. “Your Turn” from “Example 1” on page 293 of the textbook
    1. For the equation the non-permissible values will occur when cot x is undefined and when sin x = 0.

       
      cot x is undefined at {x = nπ, n ∈ I, x ∈ R}.

       
      sin x = 0 at {x = nπ, n ∈ I, x ∈ R}.

      Thus, the non-permissible values are {x ≠ nπ, n ∈ I, x ∈ R}.
    2. Substituting x = 45° into the equation gives the following:

      LS RS




      Using 45° in the equation yields the same answer on both sides of the equation. Based on this, the equation could be an identity.

      Substituting in the equation gives the following:

      LS RS



      Using in the equation yields the same answer on both sides of the equation. Based on this, the equation could be an identity.
    3. The graph shows the two equations: y equals cotangent x and y equals cosine x over sine x. The two equations have undefined values at 0, 180 degrees, 360 degrees, and so on, and overlap completely over the domain of –360 degrees to 360 degrees.

      Based on the information provided in the graph, the equation could be an identity.



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