How to express the sine function in c language

There are three ways to express the sine function in the C language: calling the mathematical library function sin() can directly calculate the sine value; using Taylor expansion to approximate the sine value, which has high accuracy for small angle values; using search The table stores precomputed sine values ​​and is suitable for applications requiring high performance and lower accuracy.

Representation of sine function in C language

Directly call the math library function

In C language, you can use the sin() function in the math.h library to directly calculate the sine value. The function prototype is as follows:

<code class="c">double sin(double x);</code>

Among them, x is the angle value in radian system, and the return value is the sine value of the angle.

Using Taylor expansion

You can use Taylor expansion to approximate the sine function. The Taylor expansion is very accurate for small angle values.

For the angle x, the Taylor expansion of the sine function is:

<code>sin(x) = x - (x^3) / 3! + (x^5) / 5! - (x^7) / 7! + ...</code>

This expansion can be truncated to finite terms to obtain an approximation. For example, truncated to three terms can be obtained:

<code class="c">double sin(double x) {
  return x - (x*x*x) / 6.0;  // 截断到三项
}</code>

Using a lookup table

For applications that require high performance and low accuracy, you can use a lookup table to store the pre-calculated sine value. Lookup tables can be optimized through linear interpolation or data structures such as hash tables.

Sample Code

The following C code demonstrates how to calculate the sine value using the sin() function:

<code class="c">#include <stdio.h>
#include <math.h>

int main() {
  double angle = M_PI / 3;  // 60 度

  // 使用 sin() 函数计算正弦值
  double sin_value = sin(angle);

  // 打印结果
  printf("正弦值: %.2f\n", sin_value);

  return 0;
}</code>

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