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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