!! used as default html header if there is none in the selected theme. OEF Inverse trigonometric functions

OEF Inverse trigonometric functions --- Introduction ---

This module actually contains 10 exercises on inverse trigonometric functions: arccos, arcsin, arctg, et leurs compositions.

arccos(cos)

Compute , writing it under the form , where and are rational numbers.

Linear arccos(cos)

For within the interval [,], one can simplify the function defined by to a linear function of the form . What is this linear function?
Write pi for .

Definition domain (Arcsin, Arccos)

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 , writing it under the form , where and are rational numbers.

arctg(tg)

Compute , writing it under the form , where and are rational numbers.

Composed differentiability

Is the function definded by differentiable in the interval [,] ?

Composed range

Consider the function defined by . Determine the (maximal) interval of definition and the image interval of .
To give your reply, let (open or closed), (open or closed). Write "pi", "F" or "-F" to designate , or .

Définition et image I

Choisissez les intervalles les plus pertinents dans les énoncés suivants.
La fonction est définie sur l'intervalle .
Son image est .
Cette fonction est dérivable sur .

Définition et image II

Choisissez les intervalles les plus pertinents dans les énoncés suivants.
La fonction est définie sur l'intervalle .
Son image est .
On a pour .

Définition et image III

Choisissez les intervalles les plus pertinents dans les énoncés suivants.
La fonction est définie sur l'intervalle .
Son image est .
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