Module 5: Lesson 1

 

Self-Check 1

 

Questions 1.a., 1.b., 2.a., 2.b., 2.c., 4, and 8 on pages 262 to 264 of the textbook

  1.  


    2. The angle that will be found when using this ratio is θ ≈ −59.5°. However, this angle would be in quadrant 4 and not in quadrant 2, as the question asks. As a result, you need to use the reference angle of θ ≈ 59.5° to determine that the angle asked for in the question is θ ≈ 120.5° (180° − 59.5°).
  2.  
    1. is undefined.
  1.  
    This diagram shows a graph of the tangent of x from –360 degrees to 360 degrees. The graph indicates that the value of y when x is equal to 60 degrees in the equation is 1.732 050 8.
    Adapted from:  Pre-Calculus 12. Whitby, ON:
    McGraw-Hill Ryerson, 2011. Reproduced with permission.


    The other values of x that will result in the same answer occur at x = −300°, −120°, and 240°.
  1.  

    1. θ

      tan θ

      89.5°

      114.59

      89.9°

      572.96

      89.999°

      57 295.78

      89.999 999°

      57 295 779.51


    2. As θ approaches 90°, the values of tan θ get larger and larger, approaching infinity.

    3. θ

      tan θ

      90.5°

      −114.59

      90.01°

      −5729.58

      90.001°

      −57 295.78

      90.000 001°

      −57 295 779.51


      As θ approaches 90° from the other direction, the values of tan θ approach negative infinity.


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