Basic Combinations基本组合
Since the raising of a number n to a power p may be defined as multiplying n times itself p times, it follows that 由于将一个数n提升到幂p可以定义为将n乘以自身p次,因此可以得出
![]() The rule for raising a power to a power can also be deduced 幂的幂法则也可以推导出来
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Powers of Ten十的幂
For very large or very small numbers, it convenient to use the "scientific notation", i.e., to express the numbers in terms of a power of 10. Standard prefixes are used to denote certain powers of 10: 对于非常大或非常小的数,使用“科学记数法”会更方便,即用10的幂来表示这些数。常用的前缀用于表示特定的10的幂:
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Radical Combinations自由基组合
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Euler Relationship欧拉关系
The trigonometric functions are related to a complex exponential by the Euler relationship 三角函数与复指数之间存在欧拉关系
![]() From these relationships the trig functions can be expressed in terms of the complex exponential: 从这些关系可以将三角函数用复指数表示为:
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Hyperbolic Functions双曲函数
The hyperbolic functions can be defined in terms of exponentials. 双曲函数可以用指数函数来定义。
![]() There are closed-form expressions for the inverse hyperbolic functions: 反双曲函数有闭式表达式:
![]() An application of the hyperbolic tangent is in calculating the speed of ocean waves. The hyperbolic cosine and its inverse are encountered in fluid friction in the case of quadratic drag. 双曲正切函数的应用之一是计算海洋波速。在二次阻力情况下,双曲余弦及其反函数会出现在流体摩擦中。
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