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I Characteristics of trigonometric function compositions like sin(sin(x))

  1. Mar 12, 2017 #1
    Hello,
    Are there any particular properties, indentities or usages of composite trigonometric functions, say sin(sinx) or cos(sin(x))?
     
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  3. Mar 12, 2017 #2

    BvU

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    Hi d5,

    Not many I should think. Usually the argument of a goniometric function is an angle and the result is a number, not an angle.
    But it's always nice to have students sink their teeth in such a contraption.
     
    Last edited: Mar 13, 2017
  4. Mar 13, 2017 #3
    Well, I have just found on the web that composite trigonometric functions can be applied in substitutions, for example: √1-9x^2 can be replaced to sin(arccos 3x).Is it useful somehow?
     
  5. Mar 13, 2017 #4

    BvU

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    This is a combination of a goniometric function acting on the result of an inverse goniometric function. Makes sense.
     
  6. Mar 13, 2017 #5
    OK. By the way, is there any difference between goniometric functions and trigonometric functions? or they are just two names of the same thing?
     
  7. Mar 13, 2017 #6

    BvU

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    Same thing
     
  8. Mar 13, 2017 #7

    BvU

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    Not completely fair: a sine is the ratio of the lengths of two sides. One can consider an angle as the ratio of arc length to radius....
     
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