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

Tags:
1. Mar 12, 2017

### ddddd28

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

2. Mar 12, 2017

### 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.

Last edited: Mar 13, 2017
3. Mar 13, 2017

### 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?

4. Mar 13, 2017

### BvU

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

5. Mar 13, 2017

### 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?

6. Mar 13, 2017

### BvU

Same thing

7. Mar 13, 2017

### BvU

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....