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OEF arccos
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. interactive exercises, online calculators and plotters, mathematical recreation and games
Keywords: interactive mathematics, interactive math, server side interactivity, analysis, arccos, acos, arcsin, asin, arctan, atan, arctg