mf_sin.hlp

是一个经济学管理应用软件 很难找的 但是经济学学生又必须用到

{smcl}
{* 25mar2005}{...}
{cmd:help mata sin()}
{hline}
{* index trigonometric functions}{...}
{* index hyperbolic functions}{...}
{* index sin()}{...}
{* index cos()}{...}
{* index tan()}{...}
{* index asin()}{...}
{* index acos()}{...}
{* index atan()}{...}
{* index atan2()}{...}
{* index asinr()}{...}
{* index acosr()}{...}
{* index atanr()}{...}
{* index arg()}{...}
{* index sinh()}{...}
{* index cosh()}{...}
{* index tanh()}{...}
{* index asinh()}{...}
{* index acosh()}{...}
{* index atanh()}{...}
{* index pi()}{...}

{title:Title}

{p 4 4 2}
{bf:[M-5] sin() -- Trigonometric and hyperbolic functions}


{title:Syntax}

{p 8 12 2}
	{it:numeric matrix} {cmd:sin(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:cos(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:tan(}{it:numeric matrix Z}{cmd:)} 


{p 8 12 2}
	{it:numeric matrix} {cmd:asin(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:acos(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:atan(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:real matrix}{bind:    }{cmd:atan2(}{it:real matrix X}{cmd:,} {it:real matrix Y}{cmd:)}


{p 8 12 2}
	{it:real matrix}{bind:    }{cmd:asinr(}{it:real matrix R}{cmd:)}

{p 8 12 2}
	{it:real matrix}{bind:    }{cmd:acosr(}{it:real matrix R}{cmd:)}

{p 8 12 2}
	{it:real matrix}{bind:    }{cmd:atanr(}{it:real matrix R}{cmd:)}


{p 8 12 2}
	{it:real matrix}{bind:    }{cmd:arg(}{it:complex matrix Z}{cmd:)} 


{p 8 12 2}
	{it:numeric matrix} {cmd:sinh(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:cosh(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:tanh(}{it:numeric matrix Z}{cmd:)}


{p 8 12 2}
	{it:numeric matrix} {cmd:asinh(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:acosh(}{it:numeric matrix Z}{cmd:)}

{p 8 12 2}
	{it:numeric matrix} {cmd:atanh(}{it:numeric matrix Z}{cmd:)}


{p 8 12 2}
	{it:real scalar}{bind:    }{cmd:pi()}


{title:Description}

{p 4 4 2}
        {cmd:sin(}{it:Z}{cmd:)}, {cmd:cos(}{it:Z}{cmd:)}, and
        {cmd:tan(}{it:Z}{cmd:)} return the appropriate trigonometric function.
        Angles are measured in radians.  All return real if argument is real,
        complex if argument is complex.

{p 4 4 2}
        {cmd:asin(}{it:Z}{cmd:)} returns arcsine in the range -pi/2 to pi/2.
        Returned value is real if argument is real, complex if argument is
        complex.

{p 4 4 2}
        {cmd:acos(}{it:Z}{cmd:)} returns arccosine in the range 0 to pi.
        Returned value is real if argument is real, complex if argument is
        complex.

{p 4 4 2}
	{cmd:atan(}{it:Z}{cmd:)} returns arctangent in the range -pi/2 to pi/2.
        Returned value real if argument is real, complex if argument is
        complex.

{p 4 4 2}
        Warning:  {cmd:asin()}, {cmd:acos()}, and {cmd:atan()} base their
        result on whether the input is real or complex.  Thus 
        {cmd:acos(2)} == . while {cmd:acos(2+0i)} == -1.317i.

{p 4 4 2}
        {cmd:atan2(}{it:x}{cmd:,} {it:y}{cmd:)} returns the radian value 
        in the range (-pi, pi] of the angle of the vector determined by
        ({it:x},{it:y}); the result being in the range [0,pi] for 
        quadrants 1 and 2 and [0,-pi) in quadrants 4 and 3.  Note that {it:x}
        and {it:y} are real; also see related function {cmd:arg()} below;
        {cmd:atan2(}{it:x}{cmd:,} {it:y}{cmd:)} is equivalent to
        {cmd:arg(C(}{it:x}{cmd:,} {it:y}{cmd:))}.


{p 4 4 2}
        {cmd:asinr(}{it:R}{cmd:)}, {cmd:acosr(}{it:R}{cmd:)}, and
        {cmd:atanr(}{it:R}{cmd:)} the real-only variants of {cmd:asin()},
        {cmd:acos()}, and {cmd:atan()}.  {cmd:asin()}, {cmd:acos()}, and
        {cmd:atan()} examine the received argument and, if it is real, call
        the appropriate real function.  Thus use of {cmd:asinr()},
        {cmd:acosr()}, and {cmd:atanr()} in place of {cmd:asin()},
        {cmd:acos()}, and {cmd:atan()} when arguments are known to be real
        will speed execution, but not by much.  We recommend use of
        {cmd:asin()}, {cmd:acos()}, and {cmd:atan()} in all cases.


{p 4 4 2}
        {cmd:arg(}{it:Z}{cmd:)} returns the arctangent of
        Im({it:Z})/Re({it:Z}) in the correct quadrant, the result being in the
        range (-pi, pi]; [0,pi] in quadrants 1 and 2 and [0,-pi) in quadrants
        4 and 3.  Also see related function {cmd:atan2()} above;
        {cmd:arg(}{it:Z}{cmd:)} is equivalent to 
	{cmd:atan2(Re(}{it:Z}{cmd:), Im(}{it:Z}{cmd:))}.


{p 4 4 2}
        {cmd:sinh(}{it:Z}{cmd:)}, {cmd:cosh(}{it:Z}{cmd:)}, and
        {cmd:tanh(}{it:Z}{cmd:)} return the hyperbolic sine, cosine, and
        tangent, respectively.  Returned value is real if argument is real,
        complex if complex.

{p 4 4 2}
        {cmd:asinh(}{it:Z}{cmd:)}, {cmd:acosh(}{it:Z}{cmd:)}, and
        {cmd:atanh(}{it:Z}{cmd:)} return the inverse hyperbolic sine, cosine,
        and tangent, respectively.  Returned value is real if argument is
        real, complex if complex.  See warning above for {cmd:asin()}, etc.
        This warning applies here.


{p 4 4 2}
	{cmd:pi()} returns the value of pi.


{title:Conformability}

{p 4 4 2}
{cmd:atan2(}{it:x}{cmd:,} {it:y}{cmd:)}:
{p_end}
	{it:x}:  {it:r1 x c1}
	{it:y}:  {it:r2 x c2}, {it:x} and {it:y} r-conformable
   {it:result}:  max({it:r1},{it:r2}) {it:x} max({it:c1},{it:c2})

{p 4 4 2}
{cmd:pi()} returns a 1 {it:x} 1 scalar.

{p 4 4 2}
All other functions return a matrix of the same dimension as input,
containing element-by-element calculated results.


{title:Diagnostics}

{p 4 4 2}
        {cmd:tan(}{it:Z}{cmd:)} returns missing when
        {cmd:cos(}{it:Z}{cmd:)}==0.

{p 4 4 2}
	All functions return missing for real arguments when the result 
	would be complex, but return the appropriate complex result when 
	given a complex argument.


{title:Source code}

{p 4 4 2}
{view asin.mata, adopath asis:asin.mata},
{view acos.mata, adopath asis:acos.mata},
{view atan.mata, adopath asis:atan.mata},
{view sinh.mata, adopath asis:sinh.mata},
{view cosh.mata, adopath asis:cosh.mata},
{view tanh.mata, adopath asis:tanh.mata},
{view asinh.mata, adopath asis:asinh.mata},
{view acosh.mata, adopath asis:acosh.mata},
{view atanh.mata, adopath asis:atanh.mata},
{view pi.mata, adopath asis:pi.mata};
remaining functions are built-in.


{title:Also see}

{p 4 13 2}
Manual:  {hi:[M-5] sin()}

{p 4 13 2}
Online:  help for 
{bf:{help m4_scalar:[M-4] scalar}}
{p_end}