Solutions to Questions on Trigonometric Functions

Here are given the solutions to the questions in Graphs of Basic Trigonometric Functions. For each trigonometric function is given the domain, range, period and asymptotes (if any). These properties are necessary to understand the graphs of the trigonometric functions.

  1. f(x) = sinx(x)
    • domain : (-infinity , +infinity)
    • range : [-1 , 1]
    • period : 2Pi


  2. f(x) = cos(x)
    • domain : (-infinity , +infinity)
    • range : [-1 , 1]
    • period : 2Pi


  3. f(x) = tan(x)
    • domain : all real numbers except Pi/2 + k*Pi where k is an integer.
    • range : (-infinity , +infinity)
    • period : Pi
    • vertical asymptotes at x = Pi/2 + k*Pi, k is an integer.


  4. f(x) = cot(x)
    • domain : all real numbers except k*Pi where k is an integer.
    • range : (-infinity , +infinity)
    • period : Pi
    • vertical asymptotes at x = k*Pi, k is an integer.


  5. f(x) = sec(x)
    • domain : all real numbers except Pi/2 + k*Pi where k is an integer.
    • range : (-infinity , -1] U [1 , +infinity)
    • period : 2Pi
    • vertical asymptotes at x = Pi/2 + k*Pi, k is an integer.


  6. f(x) = csc(x)
    • domain : all real numbers except k*Pi where k is an integer.
    • range : (-infinity , -1] U [1 , +infinity)
    • period : 2Pi
    • vertical asymptotes at x = k*Pi, k is an integer.


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

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Updated: 25 November 2007 (A Dendane)