Graphs of Basic Trigonometric Functions

The graphs and properties such as domain, range, vertical asymptotes of the 6 basic trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) are explored using an applet.



Once you finish the present tutorial, you may want to go through a self test on trigonometric graphs. If needed, Free graph paper is available.

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TUTORIAL:click on the button above "click here to start" and MAXIMIZE the applet window obtained.

  1. Click on the radio button of sin (x) and use the graph to determine the range of sin (x). What is the domain of sin (x)?

    Answer

  2. Click on the radio button of cos (x) and use the graph to determine the range of cos (x). What is the domain of cos (x)?

    Answer

  3. Click on the radio button of tan (x). The red broken lines are the vertical asymptotes for the graph of tan (x).  Use the fact that

    tan(x) = sin(x) / cos(x)

    to find the domain of tan(x). (Hint: find the zeros of the denominator and exclude them from the set of real numbers). The same zeros of the denominator gives you equations of the vertical asymptotes. Find the vertical asymptotes. Now use the graph of tan (x) to check your answers, domain and vertical asymptotes, found analytically. Use the fact that vertical asymptotes means an increases or decreases without bound to find the range of tan(x).

    Answer

  4. Click on the radio button of cot(x). The red broken lines are the vertical asymptotes for the graph of cot(x). Use the fact that

    cot(x) = cos(x) / sin(x)

    to find the domain of cot(x). (Hint: find the zeros of the denominator and exclude them from the set of real numbers). The same zeros of the denominator gives you equations of the vertical asymptotes. Find the vertical asymptotes. Now use the graph of cot(x) to check your answers, domain and vertical asymptotes, found analytically. Use the concepts of vertical asymptotes to determine the range of cot(x).

    Answer

  5. Click on the radio button of sec(x). The red broken lines are the vertical asymptotes for the graph of sec(x).  Use the fact that

    sec(x) = 1 / cos(x)

    to find the domain of sec(x) and vertical asymptotes for the graph of sec(x). Now use the graph of sec(x) to check your answers, domain and vertical asymptotes, found analytically. Use the concepts of vertical asymptotes to determine the range of sec(x).

    Answer

  6. Click on the radio button of csc(x). The red broken lines are the vertical asymptotes for the graph of csc(x).  Use the fact that

    csc(x) = 1 / sin(x)

    to find the domain of csc(x). (Hint: find the zeros of the denominator and exclude them). The same zeros of the denominator gives you equations of the vertical asymptotes. Find the vertical asymptotes. Now use the graph of csc(x) to check your answers, domain and vertical asymptotes, found analytically. Use the concepts of vertical asymptotes to determine the range of csc(x).

Answer

More references and links related to trigonometric functions and their properties.


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Updated: 2 April 2013

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