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<h1 id="firstHeading" class="firstHeading">casinf, casin, casinl</h1> <table class="t-dcl-begin"> <tr class="t-dsc-header"> <th> Defined in header <code><complex.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">float complex casinf( float complex z );</pre>
</td> <td> (1) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">double complex casin( double complex z );</pre>
</td> <td> (2) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">long double complex casinl( long double complex z );</pre>
</td> <td> (3) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dsc-header"> <th> Defined in header <code><tgmath.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">#define asin( z )</pre>
</td> <td> (4) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> </table> <div class="t-li1">
<span class="t-li">1-3)</span> Computes the complex arc sine of <code>z</code> with branch cuts outside the interval [−1,+1] along the real axis.</div> <div class="t-li1">
<span class="t-li">4)</span> Type-generic macro: If <code>z</code> has type <code><span class="kw4">long</span> <span class="kw4">double</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>casinl</code> is called. if <code>z</code> has type <code><span class="kw4">double</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>casin</code> is called, if <code>z</code> has type <code><span class="kw4">float</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>casinf</code> is called. If <code>z</code> is real or integer, then the macro invokes the corresponding real function (<code>asinf</code>, <code><a href="http://en.cppreference.com/w/c/numeric/math/asin"><span class="kw672">asin</span></a></code>, <code>asinl</code>). If <code>z</code> is imaginary, then the macro invokes the corresponding real version of the function <code><a href="../math/asinh" title="c/numeric/math/asinh">asinh</a></code>, implementing the formula \(\small \arcsin({\rm i}y) = {\rm i}{\rm arsinh}(y)\)arcsin(iy) = i arsinh(y), and the return type of the macro is imaginary.</div> <h3 id="Parameters"> Parameters</h3> <table class="t-par-begin"> <tr class="t-par"> <td> z </td> <td> - </td> <td> complex argument </td>
</tr>
</table> <h3 id="Return_value"> Return value</h3> <p>If no errors occur, complex arc sine of <code>z</code> is returned, in the range of a strip unbounded along the imaginary axis and in the interval [−π/2; +π/2] along the real axis.</p>
<p>Errors and special cases are handled as if the operation is implemented by <code><span class="sy2">-</span>I <span class="sy2">*</span> <a href="http://en.cppreference.com/w/c/numeric/complex/casinh"><span class="kw799">casinh</span></a><span class="br0">(</span>I<span class="sy2">*</span>z<span class="br0">)</span></code></p>
<h3 id="Notes"> Notes</h3> <p>Inverse sine (or arc sine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞,-1) and (1,∞) of the real axis.</p>
<p>The mathematical definition of the principal value of arc sine is \(\small \arcsin z = -{\rm i}\ln({\rm i}z+\sqrt{1-z^2})\)arcsin z = -<i>i</i>ln(<i>i</i>z + <span class="t-mrad"><span>√</span><span>1-z<sup class="t-su">2</sup></span></span>) For any z, \(\small{ \arcsin(z) = \arccos(-z) - \frac{\pi}{2} }\)arcsin(z) = acos(-z) -</p>
<span><span>π</span><span>/</span><span>2</span></span> <h3 id="Example"> Example</h3> <div class="t-example"> <div class="c source-c"><pre data-language="c">#include <stdio.h>
#include <math.h>
#include <complex.h>
int main(void)
{
double complex z = casin(-2);
printf("casin(-2+0i) = %f%+fi\n", creal(z), cimag(z));
double complex z2 = casin(conj(-2)); // or CMPLX(-2, -0.0)
printf("casin(-2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
// for any z, asin(z) = acos(-z) - pi/2
double pi = acos(-1);
double complex z3 = csin(cacos(conj(-2))-pi/2);
printf("csin(cacos(-2-0i)-pi/2) = %f%+fi\n", creal(z3), cimag(z3));
}</pre></div> <p>Output:</p>
<div class="text source-text"><pre data-language="c">casin(-2+0i) = -1.570796+1.316958i
casin(-2-0i) (the other side of the cut) = -1.570796-1.316958i
csin(cacos(-2-0i)-pi/2) = 2.000000+0.000000i</pre></div> </div> <h3 id="References"> References</h3> <ul>
<li> C11 standard (ISO/IEC 9899:2011): </li>
<ul>
<li> 7.3.5.2 The casin functions (p: 190) </li>
<li> 7.25 Type-generic math <tgmath.h> (p: 373-375) </li>
<li> G.7 Type-generic math <tgmath.h> (p: 545) </li>
</ul>
<li> C99 standard (ISO/IEC 9899:1999): </li>
<ul>
<li> 7.3.5.2 The casin functions (p: 172) </li>
<li> 7.22 Type-generic math <tgmath.h> (p: 335-337) </li>
<li> G.7 Type-generic math <tgmath.h> (p: 480) </li>
</ul>
</ul> <h3 id="See_also"> See also</h3> <table class="t-dsc-begin"> <tr class="t-dsc"> <td> <div><a href="cacos" title="c/numeric/complex/cacos"> <span class="t-lines"><span>cacos</span><span>cacosf</span><span>cacosl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex arc cosine <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="catan" title="c/numeric/complex/catan"> <span class="t-lines"><span>catan</span><span>catanf</span><span>catanl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex arc tangent <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="csin" title="c/numeric/complex/csin"> <span class="t-lines"><span>csin</span><span>csinf</span><span>csinl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex sine <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="../math/asin" title="c/numeric/math/asin"> <span class="t-lines"><span>asin</span><span>asinf</span><span>asinl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td colspan="2"> <span><a href="https://en.cppreference.com/w/cpp/numeric/complex/asin" title="cpp/numeric/complex/asin">C++ documentation</a></span> for <code>asin</code> </td>
</tr> </table> <div class="_attribution">
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