cosecant

简明释义

英[kəʊˈsiːkənt]美[koʊˈsiːkənt]

n. [数] 余割

英英释义

单词用法

同义词

反义词

例句

1.The results of flat-top wave beam and cosecant square wave beam, which are gained using this method, are fairly good, testifying this method is effective in beam shaping of conformal arrays.

运用此方法得到共形圆柱阵列的平顶波束和余割平方波束方向图，效果较好，证明此方法对于共形阵列是有效的。

2.Cosecant Beam Generation Program for computing Phase distribution function and Radiation pattern.

余割波束生成程序的计算相分布函数和辐射模式。

3.The inspection method of cosecant beam antenna is discussed in depth in this paper.

对余割波束天线的检测方法进行了较深入的探讨。

4.The results of flat-top wave beam and cosecant square wave beam, which are gained using this method, are fairly good, testifying this method is effective in beam shaping of conformal arrays.

运用此方法得到共形圆柱阵列的平顶波束和余割平方波束方向图，效果较好，证明此方法对于共形阵列是有效的。

5.To find the cosecant 余割, you can use the formula: cosec(θ) = 1/sin(θ).

要找到cosecant 余割，你可以使用公式：cosec(θ) = 1/sin(θ)。

6.The cosecant 余割 function is undefined for angles where sine equals zero.

当正弦为零时，cosecant 余割 函数是未定义的。

7.In trigonometry, the cosecant 余割 of an angle is the reciprocal of its sine.

在三角学中，角的cosecant 余割 是其正弦的倒数。

8.The cosecant 余割 function is often used in calculus to solve integrals involving trigonometric functions.

在微积分中，cosecant 余割 函数常用于求解涉及三角函数的积分。

9.In a right triangle, the cosecant 余割 of an angle can be calculated by dividing the length of the hypotenuse by the length of the opposite side.

在直角三角形中，可以通过将斜边的长度除以对边的长度来计算一个角的cosecant 余割。

作文

In the world of mathematics, particularly in trigonometry, the term cosecant refers to a specific function that is essential for understanding relationships between angles and lengths in right triangles. The cosecant is defined as the reciprocal of the sine function, which means that if you know the sine of an angle, you can easily find the cosecant by taking the inverse of that value. This relationship is crucial when solving various problems involving triangles, especially in fields such as engineering, physics, and architecture.To illustrate this concept further, let's consider a right triangle where one of the angles is denoted as θ (theta). The sine of this angle is calculated as the ratio of the length of the opposite side to the hypotenuse. Therefore, the cosecant, which is the reciprocal of the sine, is calculated as the ratio of the hypotenuse to the length of the opposite side. Mathematically, this can be expressed as:
cosecant(θ) = 1/sine(θ)Understanding the cosecant function is not just about memorizing its definition; it also involves recognizing how it fits into the broader context of trigonometric identities and equations. For instance, the cosecant function, along with other trigonometric functions like cosine and tangent, can be used to derive various identities that are useful in simplifying complex equations. One such identity is the Pythagorean identity, which relates the squares of the sine and cosine functions. By manipulating these identities, mathematicians can solve for unknown variables in a variety of applications.Moreover, the cosecant function has important properties that make it unique among trigonometric functions. For example, the cosecant is undefined for angles where the sine is equal to zero, such as at 0 degrees or 180 degrees. This characteristic leads to vertical asymptotes in the graph of the cosecant function, which is a crucial aspect to consider when analyzing its behavior visually. The graph of the cosecant function shows periodicity, meaning it repeats its values at regular intervals, which is a fundamental property of all trigonometric functions.In practical applications, the cosecant can be utilized in various real-world scenarios. For instance, in physics, when analyzing forces acting at angles, the cosecant can help determine the component of force acting in a particular direction. In architecture, understanding the cosecant aids in calculating the heights of structures based on angles of elevation and distances.In conclusion, the term cosecant is not just a mathematical term; it represents a vital concept in trigonometry that connects angles and lengths in right triangles. By understanding its definition, properties, and applications, one can appreciate the significance of the cosecant in both theoretical and practical contexts. As we continue to explore the vast world of mathematics, the cosecant will undoubtedly remain a key player in our understanding of geometry and beyond.

在数学的世界中，特别是在三角学中，术语余弦函数指的是一个特定的函数，它对于理解直角三角形中角度和长度之间的关系至关重要。余弦函数被定义为正弦函数的倒数，这意味着如果你知道一个角的正弦值，你可以通过取该值的倒数来轻松找到余弦函数。这种关系在解决涉及三角形的各种问题时是至关重要的，尤其是在工程、物理和建筑等领域。为了进一步说明这个概念，我们考虑一个直角三角形，其中一个角用θ（希腊字母theta）表示。这个角的正弦是通过对边的长度与斜边的长度之比来计算的。因此，余弦函数，即正弦的倒数，是通过斜边与对边的长度之比来计算的。从数学上讲，可以表达为：
余弦函数(θ) = 1/正弦(θ)理解余弦函数不仅仅是记住它的定义；它还涉及到认识到它如何融入更广泛的三角恒等式和方程中。例如，余弦函数与其他三角函数如余弦和正切一起，可以用于推导各种恒等式，这些恒等式在简化复杂方程时非常有用。其中一个恒等式是勾股恒等式，它将正弦和余弦函数的平方联系起来。通过操作这些恒等式，数学家可以求解各种应用中的未知变量。此外，余弦函数具有使其在三角函数中独特的重要属性。例如，当正弦等于零时，如在0度或180度时，余弦函数是未定义的。这一特性导致了余弦函数图形中的垂直渐近线，这是分析其视觉行为时必须考虑的关键方面。余弦函数的图形显示出周期性，这意味着它在规则的间隔内重复其值，这是所有三角函数的基本属性。在实际应用中，余弦函数可以用于各种现实场景。例如，在物理学中，当分析作用在角度上的力时，余弦函数可以帮助确定在特定方向上作用的力的分量。在建筑学中，了解余弦函数有助于根据高度和距离计算结构的高度。总之，术语余弦函数不仅仅是一个数学术语；它代表了三角学中的一个重要概念，连接了直角三角形中的角度和长度。通过理解其定义、属性和应用，人们可以欣赏到余弦函数在理论和实践背景中的重要性。当我们继续探索广阔的数学世界时，余弦函数无疑将继续成为我们理解几何学及其他领域的关键角色。