arcsine

简明释义

英[ˈɑrkˌsaɪn]美[ˈɑrkˌsaɪn]

n. 反正弦

英英释义

单词用法

同义词

反义词

例句

1.Fast and accurate computation of the arcsine function in a modern engineering has been used widely.

快速精确的反正弦函数运算在现代工程中应用广泛。

2.The inverse function of that restricted sine function is called the arcsine function.

被限定的正弦函数之反函数叫做反正弦函数。

3.Expression to compute the arcsine of.

要计算反正弦的表达式。

4.Computes the arcsine of the specified argument.

计算指定参数的反正弦。

5.Returns the arcsine of a number.

返回数字的反正弦值。

6.Fast and accurate computation of the arcsine function in a modern engineering has been used widely.

快速精确的反正弦函数运算在现代工程中应用广泛。

7.We extend the first arcsine law to an asymmetry walk model, and get its limit behavior.

我们把第一反正弦律推广到不对称游动的模型，并得到了其极限性质。

8.To find the angle whose sine is 0.5, we can use the arcsine function.

要找到正弦值为0.5的角度，我们可以使用反正弦函数。

9.When solving for angles in a right triangle, the arcsine can be very useful.

在解决直角三角形的角度时，反正弦非常有用。

10.In trigonometry, the arcsine of a value gives the angle in radians.

在三角学中，某个值的反正弦给出的是以弧度表示的角度。

11.The calculator has an arcsine button for quick access to this function.

这个计算器有一个反正弦按钮，方便快速访问这个功能。

12.Using the arcsine function, we can determine the angle from the ratio of opposite to hypotenuse.

通过使用反正弦函数，我们可以根据对边与斜边的比率确定角度。

作文

In the realm of mathematics, particularly in trigonometry, the concept of the arcsine (反正弦) plays a pivotal role. The arcsine function is the inverse of the sine function, and it is essential for understanding various mathematical principles and applications. To put it simply, if you have a value of a sine function, the arcsine allows you to find the angle that corresponds to that sine value. This relationship is crucial in solving triangles, especially when dealing with right-angled triangles where one angle is known, and you need to find the other angles or side lengths.For example, consider a right triangle where one of the angles is known to have a sine value of 0.5. To find the angle itself, you would use the arcsine function. Mathematically, this is expressed as: if sin(θ) = 0.5, then θ = arcsine(0.5). The result would be 30 degrees or π/6 radians, which is a fundamental angle in trigonometry.The arcsine function is typically denoted as sin⁻¹(x), where x is the sine value. It is important to note that the output of the arcsine function is restricted to a specific range; specifically, the output will always fall within the interval [-π/2, π/2] or [-90°, 90°]. This restriction ensures that each input value corresponds to only one output angle, maintaining the function's definition as an inverse.Understanding the arcsine function is not just limited to theoretical mathematics; it has practical applications in various fields such as physics, engineering, and computer science. For instance, in physics, the arcsine can be used in wave mechanics to determine angles of incidence and reflection. Engineers often rely on the arcsine function when designing structures that require precise angles for stability and strength.Moreover, in computer graphics, the arcsine function is utilized to calculate angles for rendering objects in three-dimensional space. When developing algorithms for animations or simulations, understanding how to manipulate angles using the arcsine function becomes invaluable. In conclusion, the arcsine (反正弦) function is a fundamental concept in trigonometry that serves as the inverse of the sine function. Its ability to convert sine values back into angles makes it an essential tool for mathematicians, scientists, and engineers alike. By mastering the arcsine function, one can unlock a deeper understanding of trigonometric relationships and their applications in real-world scenarios. Whether you are solving a simple triangle or working on complex engineering problems, the arcsine function remains a vital part of the mathematical toolkit.

在数学的领域中，特别是在三角学中，arcsine（反正弦）的概念起着关键作用。arcsine函数是正弦函数的反函数，对于理解各种数学原理和应用至关重要。简单来说，如果你拥有一个正弦函数的值，arcsine可以让你找到与该正弦值对应的角度。这种关系在解决三角形时尤其重要，特别是在处理直角三角形时，当已知一个角度时，你需要找到其他角度或边长。例如，考虑一个直角三角形，其中一个角的正弦值为0.5。为了找到这个角本身，你将使用arcsine函数。在数学上，这可以表示为：如果sin(θ) = 0.5，那么θ = arcsine(0.5)。结果将是30度或π/6弧度，这是三角学中的一个基本角。arcsine函数通常表示为sin⁻¹(x)，其中x是正弦值。重要的是要注意，arcsine函数的输出被限制在一个特定的范围内；具体来说，输出将始终落在区间[-π/2, π/2]或[-90°, 90°]之间。这种限制确保每个输入值对应于唯一的输出角度，从而保持函数作为反函数的定义。理解arcsine函数不仅限于理论数学；它在物理、工程和计算机科学等多个领域具有实际应用。例如，在物理学中，arcsine可以用于波动力学中确定入射和反射角度。工程师在设计需要精确角度以确保稳定性和强度的结构时，常常依赖arcsine函数。此外，在计算机图形学中，arcsine函数用于计算三维空间中对象的角度。当开发动画或模拟的算法时，了解如何使用arcsine函数操作角度变得至关重要。总之，arcsine（反正弦）函数是三角学中的一个基本概念，它作为正弦函数的反函数。它将正弦值转换回角度的能力使其成为数学家、科学家和工程师的重要工具。通过掌握arcsine函数，人们可以深入理解三角关系及其在现实世界场景中的应用。无论你是在解决简单的三角形问题还是在处理复杂的工程问题，arcsine函数始终是数学工具箱中不可或缺的一部分。