Graphing and Trigonometric Functions: Practice Exercises

Here are various Exercises to accompany the section Graphing and Trigonometric Functions.  

Describing Trigonometric Graphs

  1. Use our transformational graphing technique to graph the following trigonometric functions from the previous Exercise:
    1. f(t) = 2sin(5(t - p/3)) - 4.
    2. g(t) = 2 - 3cos(-4t - 5p).
    3. h(t) = sin(t/2 - p)/3 + 1.
    4. k(t) = -1 - 4cos(3(t/2 + p))/5.

    Solution.

  2. Fill-in-the-blanks, putting either sin or cos into the second blank, to create a formula for a trigonometric function, then use our transformational graphing technique to graph it.

    y = __·__(__x + __) + __

    Repeat this Exercise as often as necessary until you are confident in your ability to plot basic trigonometric graphs.

    Solution.

  3. Determine the amplitude, baseline shift, and wavelength in each of the following functions.
    1.  
    2. f(t) = 2sin(5(t - p/3)) - 4.
    3. g(t) = 2 - 3cos(-4t - 5p).
    4. h(t) = sin(t/2 - p)/3 + 1.  Hint: Remember to use proper order of operations in order to interpret this expression correctly.
    5. k(t) = -1 - 4cos(3(t/2 + p))/5.

    Solution.

  4. Determine a trigonometric function which applies to each of the following situations.
    1. f is given by the following table of values:
      t f(t)
      0
      5
      10
      15
      20      		 6
      3
      6
      9
      6
    2. g(t) has the following graph:

    3. A weight is hanging on a large spring, originally at a height of 8 in. from the top of the table.  If you pull down on the spring, until it is only 4 in. off the table and let go, it will begin to oscillate from that minimum height of 4 in. to a maximum height of 12 in.  If it makes one bounce in 2 seconds, give the equation for  h(t) = height above the table after letting go.
    4. Have your partner construct a problem similar to one of parts a) - c).  Have him/her describe this situation to you, and see if you can write down a correct equation.

    Solution.

Graphing the Advanced Trigonometric Functions

  1. Explain why the amplitude of each of the advanced trigonometric functions (i.e., tan, cot, sec, and csc) is infinite.

    Solution.

  2. Use our transformational graphing technique to graph the following trigonometric functions.  Determine the baseline shift and wavelength in each case:
    1. f(t) = 3tan(2(t - p/4)) - 1.
    2. g(t) = -3cot(2(t - p/4)) - 1.
    3. h(t) = -2sec(3t - p) - 4.
    4. k(t) = csc(2(t + p/3))/5 + 1.

    Solution.

  3. Fill-in-the-blanks, putting either tan, cot, sec, or csc into the second blank, to create a formula for a trigonometric function, then use our transformational graphing technique to graph it.

    y = __·__(__x + __) + __

    Repeat this Exercise as often as necessary until you are confident in your ability to plot the advanced trigonometric functions.

    Solution.

Go to Solving Trigonometric Equations.

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