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

[ddddd28]

Hello,
Are there any particular properties, indentities or usages of composite trigonometric functions, say sin(sinx) or cos(sin(x))?

 

[BvU]

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.

 

[ddddd28]

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?

 

[BvU]

This is a combination of a goniometric function acting on the result of an inverse goniometric function. Makes sense.

 

[ddddd28]

OK. By the way, is there any difference between goniometric functions and trigonometric functions? or they are just two names of the same thing?

 

[BvU]

Same thing

 

[BvU]

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...