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

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SUMMARY

The discussion focuses on the properties and applications of composite trigonometric functions, specifically examples like sin(sin(x)) and cos(sin(x)). It highlights that while the argument of a trigonometric function typically represents an angle, composite functions can be useful in mathematical substitutions, such as replacing √(1-9x²) with sin(arccos(3x)). The conversation also clarifies that "goniometric functions" and "trigonometric functions" refer to the same mathematical concepts, emphasizing the importance of understanding these compositions in advanced mathematics.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine, cosine)
  • Familiarity with inverse trigonometric functions (arcsin, arccos)
  • Knowledge of mathematical substitutions and identities
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research the properties of composite trigonometric functions
  • Study the applications of inverse trigonometric functions in calculus
  • Explore trigonometric identities and their proofs
  • Learn about the graphical representations of composite functions
USEFUL FOR

Mathematics students, educators, and anyone interested in advanced trigonometric concepts and their applications in calculus and algebra.

ddddd28
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Hello,
Are there any particular properties, indentities or usages of composite trigonometric functions, say sin(sinx) or cos(sin(x))?
 
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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:
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?
 
This is a combination of a goniometric function acting on the result of an inverse goniometric function. Makes sense.
 
OK. By the way, is there any difference between goniometric functions and trigonometric functions? or they are just two names of the same thing?
 
Same thing
 
BvU said:
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.
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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