C++笔记，数学函数

参考链接：C++中数学函数的使用方法_cpp里指数函数-CSDN博客

头文件 <cmath> 

1. 基本的算数运算函数

1.1 sqrt() - 计算平方根

• 功能：计算一个非负实数的平方根。
• 原型：double sqrt(double x);
• 示例代码：

#include <iostream>
#include <cmath>int main() {double num = 25.0;double result = std::sqrt(num);std::cout << "The square root of " << num << " is " << result << std::endl;return 0;
}

1.2 pow() - 计算幂次方

• 功能：计算 x 的 y 次幂。
• 原型：double pow(double x, double y);
• 示例代码：

#include <iostream>
#include <cmath>int main() {double base = 2.0;double exponent = 3.0;double result = std::pow(base, exponent);std::cout << base << " raised to the power of " << exponent << " is " << result << std::endl;return 0;
}

2. 三角函数

要注意角度的单位是弧度。

若需要将角度从度转换为弧度，可以使用公式 radians = degrees * (M_PI / 180)

（在某些编译器中，M_PI 可能未定义，可以手动定义 #define M_PI 3.14159265358979323846）。

2.1 sin()、cos()、tan() - 计算正弦、余弦和正切值

• 功能：分别计算给定角度（以弧度为单位）的正弦、余弦和正切值。
• 原型：
  • double sin(double x);        对/斜
  • double cos(double x);        邻/斜
  • double tan(double x);        对/邻
• 示例代码：

#include <iostream>
#include <cmath>int main() {double angleInRadians = 1.0; // 1 弧度double sinValue = std::sin(angleInRadians);double cosValue = std::cos(angleInRadians);double tanValue = std::tan(angleInRadians);std::cout << "sin(" << angleInRadians << ") = " << sinValue << std::endl;std::cout << "cos(" << angleInRadians << ") = " << cosValue << std::endl;std::cout << "tan(" << angleInRadians << ") = " << tanValue << std::endl;return 0;
}

2.2 asin()、acos()、atan() - 计算反正弦、反余弦和反正切值

• 功能：分别计算给定值的反正弦、反余弦和反正切值，返回值为弧度。
• 原型：
  • double asin(double x);
  • double acos(double x);
  • double atan(double x);
• 示例代码：

#include <iostream>
#include <cmath>int main() {double value = 0.5;double asinValue = std::asin(value);double acosValue = std::acos(value);double atanValue = std::atan(value);std::cout << "arcsin(" << value << ") = " << asinValue << " radians" << std::endl;std::cout << "arccos(" << value << ") = " << acosValue << " radians" << std::endl;std::cout << "arctan(" << value << ") = " << atanValue << " radians" << std::endl;return 0;
}

2.3 atan2(y, x) - 计算反正切值 

功能：返回值为弧度，计算点(0，0)和(x，y)的连线与X轴正半轴的夹角，其值域为 [-π，π] （当y=0时，可以取到±π），且在第一二象限为正，在第三四象限为负。

与之类似的函数还有atan2f(y, x)、atan2d(y, x)，分别对应float类型和int类型。

示例代码：

#include <iostream>
#define M_PI       3.14159265358979323846   // piusing namespace std;int main()
{double x = 100;double y = 1;double abs1, abs2, abs3, abs4;abs1 = atan2(y, x) * 180 / M_PI;cout << "第一象限角abs1= " << abs1 << endl;abs2 = atan2(y, -x) * 180 / M_PI;cout << "第二象限角abs2= " << abs2 << endl;abs3 = atan2(-y, -x) * 180 / M_PI;cout << "第三象限角abs3= " << abs3 << endl;abs4 = atan2(-y, x) * 180 / M_PI;cout << "第四象限角abs4= " << abs4 << endl;return 0;
}

输出结果：

第一象限角abs1= 0.572939
第二象限角abs2= 179.427
第三象限角abs3= -179.427
第四象限角abs4= -0.572939

拓展：atan2与atan的区别

1. atan(x)

atan(x)表示求的是x的反正切，其返回值为[-pi/2,+pi/2]之间的一个数。

2. atan2(y,x)

当点(x, y) 落入第一象限时，atan2(y, x)的范围是 0 ~ pi/2;
当点(x, y) 落入第二象限时，atan2(y, x)的范围是 pi/2 ~ pi;
当点(x, y) 落入第三象限时，atan2(y, x)的范围是 －pi～－pi/2;
当点(x, y) 落入第四象限时，atan2(y, x)的范围是 -pi/2～0.

当 y/x > 0 时，atan(y/x)取值范围是 0 ~ pi/2；
当 y/x < 0 时，atan(y/x)取值范围是 -pi/2～0.

#include <iostream>
#include <cmath>int main() {double x = 2.0;double result = std::exp(x);std::cout << "e raised to the power of " << x << " is " << result << std::endl;return 0;
}

#include <iostream>
#include <cmath>int main() {double num = 100.0;double naturalLog = std::log(num);double commonLog = std::log10(num);std::cout << "Natural logarithm of " << num << " is " << naturalLog << std::endl;std::cout << "Common logarithm of " << num << " is " << commonLog << std::endl;return 0;
}

#include <iostream>
#include <cmath>int main() {int intNum = -5;double doubleNum = -3.14;int intAbs = std::abs(intNum);double doubleAbs = std::fabs(doubleNum);std::cout << "Absolute value of " << intNum << " is " << intAbs << std::endl;std::cout << "Absolute value of " << doubleNum << " is " << doubleAbs << std::endl;return 0;
}

#include <iostream>
#include <cmath>int main() {double num = 3.2;double ceiling = std::ceil(num);double floorValue = std::floor(num);std::cout << "Ceiling of " << num << " is " << ceiling << std::endl;std::cout << "Floor of " << num << " is " << floorValue << std::endl;return 0;
}