الرئيسية Unlabelled
http://reference.wolfram.com/language/ref/ArcSin.html
ArcSin[z]
gives the arc sine  of the complex number .

Details

Background & Context

Examples

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Basic Examples  (3)

Results are in radians:
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Plot over a subset of the reals:
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Series expansion:
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Series[ArcSin[x], {x, 0, 10}]
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Scope  (7)

Evaluate numerically:
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Evaluate for complex arguments:
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Evaluate to high precision:
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The precision of the output tracks the precision of the input:
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The precision of the output can be much lower than the precision of the input:
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Simple exact values are generated automatically:
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ArcSin[1/2]
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Parity transformation is automatically applied:
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{ArcSin[-x], ArcSin[I x]}
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ArcSin threads element-wise over lists and matrices:
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ArcSin[{0.2, 0.5, 0.8}]
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ArcSin[\!\(\*
TagBox[
RowBox[{"(", "\:f3a2", GridBox[{
{"1", 
FractionBox["1", "3"]},
{"x", 
FractionBox["1", "2"]}
},
GridBoxAlignment->{
"Columns" -> {{Left}}, "ColumnsIndexed" -> {}, 
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, 
"ItemsIndexed" -> {}},
GridBoxSpacings->{
"Columns" -> {0.28, {0.7}, 0.28}, "ColumnsIndexed" -> {}, 
"Rows" -> {0.2, {0.4}, 0.2}, "RowsIndexed" -> {}, 
"Items" -> {}, "ItemsIndexed" -> {}}], "\:f3a2", ")"}],
Function[BoxForm`e$, 
MatrixForm[BoxForm`e$]]]\) ]
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TraditionalForm formatting:
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Generalizations & Extensions  (5)

ArcSin can deal with real‐valued intervals from :
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ArcSin[Interval[{-1/3, 1/2}]]
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Infinite arguments give symbolic results:
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ArcSin can be applied to power series:
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ArcSin[x + x^2/2 + x^3/3 + O[x]^4]
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Find series expansions at branch points and branch cuts:
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Series[ArcSin[x], {x, 1, 1}]
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ArcSin threads over explicit lists as well as over sparse arrays:
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SparseArray[{{1, 1} -> 1, {1, 3} -> 1/
3, {3, 3} -> -(1/2), {4, 2} -> -1}]
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SparseArray[{{1, 1} -> 1, {1, 3} -> 1/
3, {3, 3} -> -(1/2), {4, 2} -> -1}];
ArcSin[%]
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SparseArray[{{1, 1} -> 1, {1, 3} -> 1/
3, {3, 3} -> -(1/2), {4, 2} -> -1}];
ArcSin[%];
% // MatrixForm
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Reviewed by . blogmathappily on 6:19 م Rating: 5
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