sinh

简明释义

英[ʃaɪn;sɪntʃ;saɪˈneɪtʃ]美[ʃaɪn]

abbr. 双曲正弦值；双曲正弦（hyperbolic sine）

n. （Sinh）人名；（老）辛

英英释义

单词用法

同义词

反义词

例句

1.The results show it is significant that sine-Gaussian beams, sinh-Gaussian beams and elegant sine-Gaussian beams can be regarded as the special cases of elegant sinh-Gaussian beams.

本文所得结果具有广泛的意义，因为正弦高斯光束、双曲正弦高斯光束和复宗量正弦高斯光束均可视为其特例。

2.The sinh, cosh, and tanh functions also all appear in various calculations in special and general relativity.

双曲正弦、双曲余弦和双曲正切函数也会以常见或特殊形式出现在各种计算中。

3.The results show it is significant that sine-Gaussian beams, sinh-Gaussian beams and elegant sine-Gaussian beams can be regarded as the special cases of elegant sinh-Gaussian beams.

本文所得结果具有广泛的意义，因为正弦高斯光束、双曲正弦高斯光束和复宗量正弦高斯光束均可视为其特例。

4.To find the area under a curve involving sinh, you may need to use integration techniques.

要找到与 sinh 相关的曲线下的面积，可能需要使用积分技术。

5.Graphing sinh shows a curve that resembles the shape of a sine wave but is steeper.

绘制 sinh 的图形显示出一种类似于正弦波的曲线，但更陡峭。

6.In hyperbolic functions, sinh represents the hyperbolic sine.

在双曲函数中，sinh 表示双曲正弦。

7.The value of sinh is calculated using the formula: sinh x = (e^x - e^-x) / 2.

sinh 的值是通过公式计算的：sinh x = (e^x - e^-x) / 2。

8.The derivative of sinh is cosh, which is another hyperbolic function.

sinh 的导数是 cosh，这是另一个双曲函数。

作文

In the realm of mathematics, particularly in the field of hyperbolic functions, the term sinh refers to the hyperbolic sine function. This function is defined for real numbers and is denoted mathematically as sinh(x) = (e^x - e^(-x))/2, where 'e' represents Euler's number, approximately equal to 2.71828. The sinh function is crucial in various applications, including engineering, physics, and even in certain areas of economics. To better understand the significance of sinh, let's consider its graphical representation. The graph of the sinh function is similar to that of the regular sine function, but it extends infinitely in both directions without oscillating. This unique property makes sinh particularly useful in modeling phenomena that exhibit exponential growth or decay, such as population dynamics and radioactive decay. Moreover, the sinh function is closely related to the circular functions, which are fundamental in trigonometry. For instance, just as the sine function can be derived from the unit circle, the sinh function can be derived from the hyperbola. This connection highlights the duality between circular and hyperbolic functions, which is a beautiful aspect of mathematics. In practical terms, engineers often utilize the sinh function when dealing with structures that require precise calculations regarding stress and strain. For example, when designing bridges or buildings, understanding how materials behave under various loads is vital. The sinh function helps in predicting these behaviors accurately, allowing for safer and more efficient designs. Additionally, the sinh function appears in the solutions to certain differential equations. These equations often arise in physics, particularly in the study of waves and heat conduction. By employing the sinh function, scientists can derive solutions that describe physical phenomena effectively. Furthermore, in the world of computer science, the sinh function finds its place in algorithms that require hyperbolic calculations. When working with complex data sets, particularly those involving geometric transformations or spatial analyses, the sinh function becomes an essential tool. In conclusion, the sinh function is not merely a mathematical curiosity; it plays a vital role across various disciplines. From engineering to physics and beyond, understanding sinh allows us to tackle complex problems and model real-world scenarios effectively. As we continue to explore the depths of mathematics, the importance of functions like sinh will undoubtedly grow, paving the way for innovative solutions and advancements in multiple fields. In Chinese, sinh 的中文释义是“双曲正弦函数”。它在数学和工程中具有重要应用，帮助我们理解和解决各种复杂问题。通过对 sinh 的深入研究，我们可以更好地掌握其在不同领域中的实际应用。

在数学领域，特别是在双曲函数的范畴中，术语sinh指的是双曲正弦函数。这个函数对于实数定义，并用数学表示为sinh(x) = (e^x - e^(-x))/2，其中'e'代表欧拉数，约等于2.71828。sinh函数在多个应用中至关重要，包括工程、物理学，甚至在某些经济学领域。为了更好地理解sinh的重要性，让我们考虑它的图形表示。sinh函数的图形与常规正弦函数相似，但它在两个方向上无限延伸而不振荡。这一独特属性使得sinh在建模表现出指数增长或衰减的现象时非常有用，例如人口动态和放射性衰变。此外，sinh函数与圆函数密切相关，后者在三角学中是基础。例如，正弦函数可以从单位圆中推导出来，而sinh函数可以从双曲线中推导。这种联系突显了圆函数和双曲函数之间的对偶性，这是数学的一个美丽方面。在实际应用中，工程师经常在处理需要精确计算应力和应变的结构时使用sinh函数。例如，在设计桥梁或建筑物时，理解材料在各种负载下的行为至关重要。sinh函数有助于准确预测这些行为，从而实现更安全、更高效的设计。此外，sinh函数出现在某些微分方程的解中。这些方程通常出现在物理学中，特别是在波动和热传导的研究中。通过使用sinh函数，科学家可以有效地推导出描述物理现象的解。此外，在计算机科学的世界中，sinh函数在需要双曲计算的算法中找到了它的位置。在处理复杂数据集时，特别是涉及几何变换或空间分析的数据集时，sinh函数成为一个重要工具。总之，sinh函数不仅仅是一个数学好奇心；它在多个学科中发挥着至关重要的作用。从工程到物理学及其他领域，理解sinh使我们能够有效地解决复杂问题并建模现实世界场景。随着我们继续探索数学的深度，像sinh这样的函数的重要性无疑会增加，为多个领域的创新解决方案和进步铺平道路。