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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 5c 73 65 63 74 69 6f 6e | 7b 61 63 6f 73 68 2d 2d |\section|{acosh--|
|00000010| 2d 48 79 70 65 72 62 6f | 6c 69 63 20 41 72 63 20 |-Hyperbo|lic Arc |
|00000020| 43 6f 73 69 6e 65 7d 0d | 5c 6c 61 62 65 6c 7b 66 |Cosine}.|\label{f|
|00000030| 6e 3a 61 63 6f 73 68 7d | 0d 5c 69 6e 64 65 78 7b |n:acosh}|.\index{|
|00000040| 61 63 6f 73 68 28 29 7d | 0d 5c 69 6e 64 65 78 7b |acosh()}|.\index{|
|00000050| 68 79 70 65 72 62 6f 6c | 69 63 20 61 72 63 20 63 |hyperbol|ic arc c|
|00000060| 6f 73 69 6e 65 7d 0d 5c | 69 6e 64 65 78 7b 69 6e |osine}.\|index{in|
|00000070| 76 65 72 73 65 20 68 79 | 70 65 72 62 6f 6c 69 63 |verse hy|perbolic|
|00000080| 20 63 6f 73 69 6e 65 7d | 0d 5c 69 6e 64 65 78 7b | cosine}|.\index{|
|00000090| 68 79 70 65 72 62 6f 6c | 69 63 20 63 6f 73 69 6e |hyperbol|ic cosin|
|000000a0| 65 21 69 6e 76 65 72 73 | 65 7d 0d 5c 62 65 67 69 |e!invers|e}.\begi|
|000000b0| 6e 7b 72 61 69 6c 7d 0d | 41 43 6f 73 68 20 3a 20 |n{rail}.|ACosh : |
|000000c0| 27 61 63 6f 73 68 27 20 | 27 28 27 20 28 20 53 63 |'acosh' |'(' ( Sc|
|000000d0| 61 6c 61 72 20 7c 20 4d | 61 74 72 69 78 20 29 20 |alar | M|atrix ) |
|000000e0| 27 29 27 20 3b 0d 5c 65 | 6e 64 7b 72 61 69 6c 7d |')' ;.\e|nd{rail}|
|000000f0| 0d 0d 5c 76 65 72 62 2b | 61 63 6f 73 68 2b 20 72 |..\verb+|acosh+ r|
|00000100| 65 74 75 72 6e 73 20 74 | 68 65 20 68 79 70 65 72 |eturns t|he hyper|
|00000110| 62 6f 6c 69 63 20 61 72 | 63 20 63 6f 73 69 6e 65 |bolic ar|c cosine|
|00000120| 20 6f 66 20 74 68 65 20 | 61 72 67 75 6d 65 6e 74 | of the |argument|
|00000130| 2e 20 54 68 65 20 72 65 | 74 75 72 6e 0d 76 61 6c |. The re|turn.val|
|00000140| 75 65 20 69 73 20 65 78 | 70 72 65 73 73 65 64 20 |ue is ex|pressed |
|00000150| 69 6e 20 72 61 64 69 61 | 6e 73 2e 20 20 49 66 20 |in radia|ns. If |
|00000160| 74 68 65 20 61 72 67 75 | 6d 65 6e 74 20 69 73 20 |the argu|ment is |
|00000170| 61 20 6d 61 74 72 69 78 | 2c 20 74 68 65 20 6f 70 |a matrix|, the op|
|00000180| 65 72 61 74 69 6f 6e 0d | 69 73 20 70 65 72 66 6f |eration.|is perfo|
|00000190| 72 6d 65 64 20 65 6c 65 | 6d 65 6e 74 2d 62 79 2d |rmed ele|ment-by-|
|000001a0| 65 6c 65 6d 65 6e 74 2e | 0d 0d 24 5c 4c 6f 6e 67 |element.|..$\Long|
|000001b0| 72 69 67 68 74 61 72 72 | 6f 77 24 20 54 68 69 73 |rightarr|ow$ This|
|000001c0| 20 69 73 20 6e 6f 74 20 | 61 6e 20 5c 52 4c 61 42 | is not |an \RLaB|
|000001d0| 5c 20 62 75 69 6c 74 2d | 69 6e 20 66 75 6e 63 74 |\ built-|in funct|
|000001e0| 69 6f 6e 2e 20 20 54 68 | 69 73 20 66 75 6e 63 74 |ion. Th|is funct|
|000001f0| 69 6f 6e 0d 69 73 20 6e | 6f 72 6d 61 6c 6c 79 20 |ion.is n|ormally |
|00000200| 6c 6f 61 64 65 64 20 6f | 6e 20 73 74 61 72 74 2d |loaded o|n start-|
|00000210| 75 70 20 66 72 6f 6d 20 | 74 68 65 20 5c 76 65 72 |up from |the \ver|
|00000220| 62 2b 61 63 6f 73 68 2e | 72 2b 20 66 69 6c 65 20 |b+acosh.|r+ file |
|00000230| 69 6e 20 74 68 65 0d 73 | 74 61 6e 64 61 72 64 20 |in the.s|tandard |
|00000240| 5c 76 65 72 62 2b 72 6c | 69 62 2b 20 64 69 72 65 |\verb+rl|ib+ dire|
|00000250| 63 74 6f 72 79 2e 20 55 | 73 65 20 6f 66 20 74 68 |ctory. U|se of th|
|00000260| 65 20 5c 76 65 72 62 2b | 2d 72 2b 20 6f 70 74 69 |e \verb+|-r+ opti|
|00000270| 6f 6e 2c 20 69 6e 63 6f | 72 72 65 63 74 6c 79 20 |on, inco|rrectly |
|00000280| 0d 73 65 74 74 69 6e 67 | 20 74 68 65 20 5c 76 65 |.setting| the \ve|
|00000290| 72 62 2b 52 4c 41 42 5f | 4c 49 42 5f 44 49 52 2b |rb+RLAB_|LIB_DIR+|
|000002a0| 20 65 6e 76 69 72 6f 6e | 6d 65 6e 74 61 6c 20 76 | environ|mental v|
|000002b0| 61 72 69 61 62 6c 65 2c | 20 6f 72 20 6d 6f 64 69 |ariable,| or modi|
|000002c0| 66 79 69 6e 67 0d 5c 76 | 65 72 62 2b 61 63 6f 73 |fying.\v|erb+acos|
|000002d0| 68 2e 72 2b 20 6d 61 79 | 20 6d 61 6b 65 20 74 68 |h.r+ may| make th|
|000002e0| 69 73 20 66 75 6e 63 74 | 69 6f 6e 20 75 6e 61 76 |is funct|ion unav|
|000002f0| 61 69 6c 61 62 6c 65 2e | 0d 0d 0d 5c 70 61 72 61 |ailable.|...\para|
|00000300| 67 72 61 70 68 7b 45 78 | 61 6d 70 6c 65 7d 0d 5c |graph{Ex|ample}.\|
|00000310| 69 6e 64 65 78 7b 65 78 | 61 6d 70 6c 65 20 6f 66 |index{ex|ample of|
|00000320| 20 61 63 6f 73 68 28 29 | 7d 0d 5c 69 6e 64 65 78 | acosh()|}.\index|
|00000330| 7b 61 63 6f 73 68 28 29 | 21 65 78 61 6d 70 6c 65 |{acosh()|!example|
|00000340| 7d 0d 5c 62 65 67 69 6e | 7b 76 65 72 62 61 74 69 |}.\begin|{verbati|
|00000350| 6d 7d 0d 3e 20 61 63 6f | 73 68 28 30 29 0d 20 20 |m}.> aco|sh(0). |
|00000360| 20 20 20 20 20 20 30 20 | 2b 20 31 2e 35 37 69 0d | 0 |+ 1.57i.|
|00000370| 3e 20 61 63 6f 73 68 28 | 31 2b 31 6a 29 0d 20 20 |> acosh(|1+1j). |
|00000380| 20 20 20 31 2e 30 36 20 | 2b 20 30 2e 39 30 35 69 | 1.06 |+ 0.905i|
|00000390| 0d 3e 20 61 63 6f 73 68 | 28 31 29 0d 20 20 20 20 |.> acosh|(1). |
|000003a0| 20 20 20 20 30 0d 3e 20 | 4d 61 74 20 3d 20 28 72 | 0.> |Mat = (r|
|000003b0| 61 6e 64 28 32 2c 33 29 | 2b 72 61 6e 64 28 32 2c |and(2,3)|+rand(2,|
|000003c0| 33 29 2a 28 30 2b 31 6a | 29 29 2a 35 20 0d 20 4d |3)*(0+1j|))*5 . M|
|000003d0| 61 74 20 3d 0d 20 6d 61 | 74 72 69 78 20 63 6f 6c |at =. ma|trix col|
|000003e0| 75 6d 6e 73 20 31 20 74 | 68 72 75 20 33 0d 20 20 |umns 1 t|hru 3. |
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|00000420| 20 20 20 20 20 20 20 20 | 20 30 2e 31 38 35 20 2b | | 0.185 +|
|00000430| 20 33 2e 32 37 69 0d 20 | 20 20 20 20 20 20 20 20 | 3.27i. | |
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|00000470| 20 30 2e 38 30 39 20 2b | 20 30 2e 36 34 34 69 0d | 0.809 +| 0.644i.|
|00000480| 0d 3e 20 61 63 6f 73 68 | 28 4d 61 74 29 0d 20 6d |.> acosh|(Mat). m|
|00000490| 61 74 72 69 78 20 63 6f | 6c 75 6d 6e 73 20 31 20 |atrix co|lumns 1 |
|000004a0| 74 68 72 75 20 33 0d 20 | 20 20 20 20 20 20 20 20 |thru 3. | |
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|000004c0| 20 20 20 20 20 20 20 20 | 20 20 20 31 2e 39 20 2b | | 1.9 +|
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|000004e0| 20 20 20 20 31 2e 39 20 | 2b 20 31 2e 35 32 69 0d | 1.9 |+ 1.52i.|
|000004f0| 20 20 20 20 20 20 20 20 | 20 20 32 2e 32 37 20 2b | | 2.27 +|
|00000500| 20 30 2e 30 38 38 35 69 | 20 20 20 20 20 20 20 20 | 0.0885i| |
|00000510| 20 20 20 31 2e 32 38 20 | 2b 20 30 2e 35 33 31 69 | 1.28 |+ 0.531i|
|00000520| 20 20 20 20 20 20 20 20 | 20 20 30 2e 37 35 31 20 | | 0.751 |
|00000530| 2b 20 30 2e 38 39 37 69 | 0d 5c 65 6e 64 7b 76 65 |+ 0.897i|.\end{ve|
|00000540| 72 62 61 74 69 6d 7d 0d | 0d 53 65 65 20 61 6c 73 |rbatim}.|.See als|
|00000550| 6f 3a 20 50 61 67 65 7e | 5c 70 61 67 65 72 65 66 |o: Page~|\pageref|
|00000560| 7b 66 6e 3a 61 63 6f 73 | 7d 20 5c 76 65 72 62 2b |{fn:acos|} \verb+|
|00000570| 61 63 6f 73 28 29 2b 2c | 0d 50 61 67 65 7e 5c 70 |acos()+,|.Page~\p|
|00000580| 61 67 65 72 65 66 7b 66 | 6e 3a 61 73 69 6e 68 7d |ageref{f|n:asinh}|
|00000590| 20 5c 76 65 72 62 2b 61 | 73 69 6e 68 28 29 2b 2c | \verb+a|sinh()+,|
|000005a0| 0d 50 61 67 65 7e 5c 70 | 61 67 65 72 65 66 7b 66 |.Page~\p|ageref{f|
|000005b0| 6e 3a 61 74 61 6e 68 7d | 20 5c 76 65 72 62 2b 61 |n:atanh}| \verb+a|
|000005c0| 74 61 6e 68 28 29 2b 2c | 0d 50 61 67 65 7e 5c 70 |tanh()+,|.Page~\p|
|000005d0| 61 67 65 72 65 66 7b 66 | 6e 3a 63 6f 73 68 7d 20 |ageref{f|n:cosh} |
|000005e0| 5c 76 65 72 62 2b 63 6f | 73 68 28 29 2b 2c 0d 50 |\verb+co|sh()+,.P|
|000005f0| 61 67 65 7e 5c 70 61 67 | 65 72 65 66 7b 66 6e 3a |age~\pag|eref{fn:|
|00000600| 73 69 6e 68 7d 20 5c 76 | 65 72 62 2b 73 69 6e 68 |sinh} \v|erb+sinh|
|00000610| 28 29 2b 2c 0d 50 61 67 | 65 7e 5c 70 61 67 65 72 |()+,.Pag|e~\pager|
|00000620| 65 66 7b 66 6e 3a 74 61 | 6e 68 7d 20 5c 76 65 72 |ef{fn:ta|nh} \ver|
|00000630| 62 2b 74 61 6e 68 28 29 | 2b 2e 0d 0d 5c 6e 65 77 |b+tanh()|+...\new|
|00000640| 70 61 67 65 20 0d 0d 0d | 0d |page ...|. |
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