Module 5: Lesson 1

 

Self-Check 2

 

Questions 6, 7, and C2 on pages 263 and 265 of the textbook

  1.  
    1. The diagram could look as follows:

       
      The diagram shows a circle of the equation x squared plus y squared equals 1 with a line segment drawn from the origin (also the centre of the circle) to a point on the circle labelled P (x, y). This line segment is also a radius of the circle. The distance of both the x- and y-values to the point P (x, y) are also labelled.

      Based upon this diagram, the slope of the terminal arm is
    2. Because tan θ is found by taking the ratio of the length of the opposite side divided by the length of the adjacent side,
    3. Since y is equivalent to sin x and x is equivalent to cos x,  is the same as
    4. Based on the answers in 6.b. and 6.c., you know that and that
  2.  
    3. Because tan θ is found by taking the ratio of the length of the opposite side divided by the length of the adjacent side, however, because the length of the hypotenuse is 1 unit, you know that y = sin θ and that x = cos θ. This is why you can recognize that tan θ can be written as either or as
 

C2.

 
 
  1. This diagram shows graphs of cos x and tan x.
    Adapted from: Pre-Calculus 12. Whitby, ON:
    McGraw-Hill Ryerson, 2011. Reproduced with permission. 

    Answers will vary when describing how the two functions are related. One area that you should recognize is that the tangent function has vertical asymptotes at the same values of x where the cosine function has zeros.
  2. This diagram shows graphs of sin x and tan x.
    Adapted from: Pre-Calculus 12. Whitby, ON:
    McGraw-Hill Ryerson, 2011. Reproduced with permission. 

    Answers will vary when describing how the two functions are related. One area that you should recognize is that the tangent function has zeros at the same values of x where the sine function has zeros.


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