Trig Function Series三角函数级数
Trigonometric functions can be expanded in power series, which facilitates approximations of the functions in extreme cases. The angle x must be in radians. 三角函数可以展开为幂级数，这有助于在极端情况下对函数进行近似。角度x必须以弧度为单位。
 Applications应用
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Applications of Trig Series三角级数的应用
One of the most important applications of trigonometric series is for situations involving very small angles. For such angles, the trigonmetric functions can be approximated by the first term in their series. This gives the useful small angle approximations: 三角级数最重要的应用之一是处理非常小的角度情况。对于这样的角度，三角函数可以近似为它们的级数中的第一项。这给出了有用的近似公式：
 Examples of the use of the small angle approximation are in the calculation of the period of a simple pendulum, and the calculation of the intensity minima in single slit diffraction. This approximation is used in most of the common expressions of geometrical optics which are built on the concept of surface power for lenses. 单摆的周期计算以及单缝衍射中强度极小值的计算都是小角近似的应用实例。这种近似在几何光学的大多数常见表达式中都被使用，这些表达式建立在透镜表面功率的概念之上。
This approximation sin x = x reaches a 1% error at about 14 degrees. 这个近似式sin x = x在大约14度时误差达到1%。
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