如何使用计算反正切arc（实现示例）

本文概述

什么是反正切？
反正切是切线函数的反函数。它返回切线为给定数字的角度。

文章图片
catan()是一个内置函数< complex.h> 头文件, 返回复杂反正切(或反正切)任何常数, 它根据闭合区间中的反正切线将假想轴进行划分[-i, + i](我代表iota), 用于评估复杂的对象说Z在虚轴上, 而要确定是实数还是整数的复杂对象, 则在内部调用预定义方法, 如下所示：

序号	方法	返回类型
1.	atan()函数采用数据类型为double的复数z, 它确定实复数的反正切	对于double类型的参数, 返回沿实轴[-PI / 2, + PI / 2]的范围内的复杂反正切。
2.	atanf()函数采用数据类型为float double的复数z, 它确定实复数的反正切。	对于float类型的参数, 返回沿实轴[-PI / 2, + PI / 2]的范围内的复杂反正切。
3.	atanl()函数采用数据类型为long double的复数z, 它确定实复数的反正切	对于long long类型的参数, 返回沿实轴[-PI / 2, + PI / 2]的范围内的复数反正切。
4.	catan()函数采用数据类型为double的复数z, 这也允许复数的虚部	对于类型为double的复杂对象, 返回复杂的反正切线位于沿虚轴[-i, + i]的范围内
5.	catanf()函数采用数据类型为float double的复数z, 这也允许复数的虚部	对于类型为float的复杂对象, 返回复杂的反正切线位于沿假想轴[-i, + i]的范围内
6.	catanl()函数采用数据类型为long double的复数z, 这也允许复数的虚部	返回类型为long double的复杂对象的复杂反正切位于沿着虚轴[-i, + i]的范围内

语法如下：

atan(double arg); atanf(float arg); atanl(long double arg); where arg is a floating-point valuecatan(double complex z); catanf(float complex z); catanl( long double complex z); where z is a Type – generic macro

参数：这些函数接受一个强制性参数?指定反正切。该参数可以是double, float或long double数据类型.
返回值：该函数返回复弧切线/弧切线根据传递的参数类型。
下面的程序说明了上述方法：
程序1:该程序将说明函数晒黑(), atanf()和atanl()计算浮点参数的反正切的主值。如果由于下溢而导致量程错误, 则四舍五入后将返回正确的结果。
C

//C program to illustrate the use //of functions atan(), atanf(), //and atanl() #include < math.h> #include < stdio.h> //Driver Code int main() { //For function atan() printf ( "atan(1) = %lf, " , atan (1)); printf ( " 4*atan(1)=%lf\n" , 4 * atan (1)); printf ( "atan(-0.0) = %+lf, " , atan (-0.0)); printf ( "atan(+0.0) = %+lf\n" , atan (0)); //For special values INFINITY printf ( "atan(Inf) = %lf, " , atan (INFINITY)); printf ( "2*atan(Inf) = %lf\n\n" , 2 * atan (INFINITY)); //For function atanf() printf ( "atanf(1.1) = %f, " , atanf(1.1)); printf ( "4*atanf(1.5)=%f\n" , 4 * atanf(1.5)); printf ( "atanf(-0.3) = %+f, " , atanf(-0.3)); printf ( "atanf(+0.3) = %+f\n" , atanf(0.3)); //For special values INFINITY printf ( "atanf(Inf) = %f, " , atanf(INFINITY)); printf ( "2*atanf(Inf) = %f\n\n" , 2 * atanf(INFINITY)); //For function atanl() printf ( "atanl(1.1) = %Lf, " , atanl(1.1)); printf ( "4*atanl(1.7)=%Lf\n" , 4 * atanl(1.7)); printf ( "atanl(-1.3) = %+Lf, " , atanl(-1.3)); printf ( "atanl(+0.3) = %+Lf\n" , atanl(0.3)); //For special values INFINITY printf ( "atanl(Inf) = %Lf, " , atanl(INFINITY)); printf ( "2*atanl(Inf) = %Lf\n\n" , 2 * atanl(INFINITY)); return 0; }

输出如下：

atan(1) = 0.785398, 4*atan(1)=3.141593 atan(-0.0) = -0.000000, atan(+0.0) = +0.000000 atan(Inf) = 1.570796, 2*atan(Inf) = 3.141593atanf(1.1) = 0.832981, 4*atanf(1.5)=3.931175 atanf(-0.3) = -0.291457, atanf(+0.3) = +0.291457 atanf(Inf) = 1.570796, 2*atanf(Inf) = 3.141593atanl(1.1) = 0.832981, 4*atanl(1.7)=4.156289 atanl(-1.3) = -0.915101, atanl(+0.3) = +0.291457 atanl(Inf) = 1.570796, 2*atanl(Inf) = 3.141593

程序2:该程序将说明函数catan(), catanf()和catanl()计算复数反正切的主值作为参数。
C

//C program to illustrate the use //of functions catan(), catanf(), //and catanl() #include < complex.h> #include < float.h> #include < stdio.h> //Driver Code int main() { //Given Complex Number double complex z1 = catan(2 * I); //Function catan() printf ( "catan(+0 + 2i) = %lf + %lfi\n" , creal(z1), cimag(z1)); //Complex(0, + INFINITY) double complex z2 = 2 * catan(2 * I * DBL_MAX); printf ( "2*catan(+0 + i*Inf) = %lf%+lfi\n" , creal(z2), cimag(z2)); printf ( "\n" ); //Function catanf() float complex z3 = catanf(2 * I); printf ( "catanf(+0 + 2i) = %f + %fi\n" , crealf(z3), cimagf(z3)); //Complex(0, + INFINITY) float complex z4 = 2 * catanf(2 * I * DBL_MAX); printf ( "2*catanf(+0 + i*Inf) = %f + %fi\n" , crealf(z4), cimagf(z4)); printf ( "\n" ); //Function catanl() long double complex z5 = catanl(2 * I); printf ( "catan(+0+2i) = %Lf%+Lfi\n" , creall(z5), cimagl(z5)); //Complex(0, + INFINITY) long double complex z6 = 2 * catanl(2 * I * DBL_MAX); printf ( "2*catanl(+0 + i*Inf) = %Lf + %Lfi\n" , creall(z6), cimagl(z6)); }

输出如下：

catan(+0 + 2i) = 1.570796 + 0.549306i 2*catan(+0 + i*Inf) = 3.141593+0.000000icatanf(+0 + 2i) = 1.570796 + 0.549306i 2*catanf(+0 + i*Inf) = 3.141593 + 0.000000icatan(+0+2i) = 1.570796+0.549306i 2*catanl(+0 + i*Inf) = 3.141593 + 0.000000i

程序3:该程序将说明函数catanh(), catanhf()和catanhl()计算的复弧双曲正切?沿实轴并在区间内[-i * PI / 2, + i * PI / 2]沿假想轴。
C

//C program to illustrate the use //of functionscatanh(), catanhf(), //and catanhl() #include < complex.h> #include < stdio.h> //Driver Code int main() { //Function catanh() double complex z1 = catanh(2); printf ( "catanh(+2+0i) = %lf%+lfi\n" , creal(z1), cimag(z1)); //for any z, atanh(z) = atan(iz)/i //I denotes Imaginary //part of the complex number double complex z2 = catanh(1 + 2 * I); printf ( "catanh(1+2i) = %lf%+lfi\n\n" , creal(z2), cimag(z2)); //Function catanhf() float complex z3 = catanhf(2); printf ( "catanhf(+2+0i) = %f%+fi\n" , crealf(z3), cimagf(z3)); //for any z, atanh(z) = atan(iz)/i float complex z4 = catanhf(1 + 2 * I); printf ( "catanhf(1+2i) = %f%+fi\n\n" , crealf(z4), cimagf(z4)); //Function catanh() long double complex z5 = catanhl(2); printf ( "catanhl(+2+0i) = %Lf%+Lfi\n" , creall(z5), cimagl(z5)); //for any z, atanh(z) = atan(iz)/i long double complex z6 = catanhl(1 + 2 * I); printf ( "catanhl(1+2i) = %Lf%+Lfi\n\n" , creall(z6), cimagl(z6)); }

【如何使用计算反正切arc（实现示例）】输出如下：

catanh(+2+0i) = 0.549306+1.570796i catanh(1+2i) = 0.173287+1.178097icatanhf(+2+0i) = 0.549306+1.570796i catanhf(1+2i) = 0.173287+1.178097icatanhl(+2+0i) = 0.549306+1.570796i catanhl(1+2i) = 0.173287+1.178097i