Module 5: Lesson 1

 

Self-Check 3

 

 Questions 9, 10, and 12 on pages 264 and 265 of the textbook

  1.  
    1. Because the camera makes one complete rotation in 60 s, the period should be 60 s; one complete rotation represents 360° or 2π rotations.

      The equation for the tangent function is y = tan (bt). The b value, in this case, is ; therefore, the equation for the tangent function is Using this formula, the trigonometric ratio for tangent can be used to obtain the formula for the distance:  or

    2. This diagram shows graph of y = 5 times the tangent of pi multiplied by x divided by 30. It also indicates that the value of y is 8.660254 when x is equal to 10.
    3. From the graph given in the answer to question 9.b., the distance from the midpoint of the fence is approximately 8.7 m when the time is 10 s. This can also be found by using the formula.

       
    4. If t = 15 is substituted into the equation, the following is obtained:

       


      This occurs because at t = 15 s, the camera will be pointing in a direction that is parallel to the fence. As a result, the camera would not show the fence.
  2.  
    1. Because the lighthouse makes one complete rotation in 2 min, the period is 2 min; one complete rotation represents 360° or 2π rotations.

      The equation for the tangent function is y = tan (bt). The b value, in this case, is π; therefore, the equation for the tangent function is . Using this formula, the trigonometric ratio for tangent can be used to obtain the formula for the distance:
    2. This diagram shows graph of y = 500 times the tangent of pi multiplied by x. It also indicates that the value of y is 688.19096 when x is equal to 0.3.
    3. At θ = 90°, the asymptote represents the moment when the ray of light shines in a direction that is parallel to the shore.
  1.  
    1. Andrea should get a graph that resembles a tangent function.
    2. When the sun is directly overhead, the slope will be undefined. It will represent the point on the tangent graph where the vertical asymptote appears.



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