arccos(cos)
Compute x=arc$val11($val11($val8)), writing it under the form x=$val6+$val7
, where $val6 and $val7 are rational numbers.
Linear arccos(cos)
For x within the interval [$val21,$val22], one can simplify the function $val8(x)=arc$val13($val13(x)) to a linear function of the form $val6$val9 + $val7. 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 $val32 intervals : What are their bounds (in increasing order) $val42
,
,
. if a bound is infinity, write +inf or -inf
arccos(sin)
Compute x=arc$val12($val11($val8)), writing it under the form x=$val6+$val7
, where $val6 and $val7 are rational numbers.
arctg(tg)
Compute x=arctg(tg($val8)), writing it under the form x=$val6+$val7
, where $val6 and $val7 are rational numbers.
Composed differentiability
Is the function $val8(x)=arc$val10($val11(x)) differentiable in the interval [$val17,$val18] ?
Composed range
Consider the function $val10(x) = $val17. Determine the (maximal) interval of definition I and the image interval J of $val10. To give your reply, let I=[$val6,$val7] (open or closed), J=[$val8,$val9] (open or closed). Write "pi", "F" or "-F" to designate
,
or -
.