#
OEF arccos
--- Introduction ---

This module actually contains 7 exercises on inverse trigonometric
functions:
arccos, arcsin, arctg, et leurs compositions.

### arccos(cos)

Compute x=arc(()), writing it under the form x=+, where and are rational numbers.

### Linear arccos(cos)

For x within the interval [,], one can simplify the function (x)=arc((x)) to a linear function of the form + . What is this linear function?

### Definition domain (Arcsin, Arcos)

Let
be the function defined by
.
The definition domain of
is composed of
disjoint intervals.
The definition domain is the reunion of intervals : What are their bounds (in increasing order)
,
,
. if a bound is infinity, write +inf or -inf

### arccos(sin)

Compute x=arc(()), writing it under the form x=+, where and are rational numbers.

### arctg(tg)

Compute x=arctg(tg()), writing it under the form x=+, where and are rational numbers.

### Composed differentiability

Is the function (x)=arc((x)) differentiable in the interval [,] ?

### Composed range

Consider the function (x) = . Determine the (maximal) interval of definition I and the image interval J of . To give your reply, let I=[,] (open or closed), J=[,] (open or closed). Write "`pi`", "`F`" or "`-F`" to designate , or -.
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- Description: collection of exercises on inverse trigonometric functions. Serveur Wims de l'ESPE-Nice-Toulon - Université de Nice - Sophia Antipolis
- Keywords: interactive mathematics, interactive math, server side interactivity, analysis, arccos, acos, arcsin, asin, arctan, atan, arctg