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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Description: collection of exercises on inverse trigonometric functions. interactive exercises, online calculators and plotters, mathematical recreation and games
Keywords: interactive mathematics, interactive math, server side interactivity, analysis, trigonometric_functions,trigonometry