trigonometric function

简明释义

三角函数

英英释义

例句

1.In physics, trigonometric functions 三角函数 are essential for analyzing oscillatory motion.

在物理学中，trigonometric functions 三角函数 对于分析振荡运动是必不可少的。

2.The graph of a trigonometric function 三角函数 can show periodic behavior, making it useful in modeling waves.

一个 trigonometric function 三角函数 的图形可以显示出周期性行为，这使得它在建模波动方面非常有用。

3.In calculus, we often need to differentiate a trigonometric function 三角函数 like sin(x) or cos(x).

在微积分中，我们经常需要对像 sin(x) 或 cos(x) 这样的 trigonometric function 三角函数 进行求导。

4.A trigonometric function 三角函数 such as tan(x) can be used to calculate the slope of a hill.

像 tan(x) 这样的 trigonometric function 三角函数 可以用来计算山坡的斜率。

5.To solve the triangle, we use the sine and cosine trigonometric functions 三角函数 to find unknown angles.

为了求解这个三角形，我们使用正弦和余弦 trigonometric functions 三角函数 来找到未知的角度。

作文

Trigonometric functions are fundamental in the study of mathematics, particularly in the field of geometry and calculus. These functions relate the angles of a triangle to the lengths of its sides, providing essential tools for solving various problems in science and engineering. The primary trigonometric functions include sine, cosine, and tangent, each playing a crucial role in different applications. For instance, the sine function, denoted as sin(x), is defined as the ratio of the opposite side to the hypotenuse in a right triangle. Similarly, the cosine function, represented as cos(x), is the ratio of the adjacent side to the hypotenuse. The tangent function, tan(x), is the ratio of the sine and cosine functions, which can also be expressed as the ratio of the opposite side to the adjacent side. Understanding these trigonometric functions is vital for students and professionals in fields such as physics, engineering, and computer science. In physics, for example, these functions help describe oscillatory motions, wave patterns, and circular movements. Engineers utilize trigonometric functions to analyze forces, design structures, and create models that simulate real-world scenarios. Moreover, in computer graphics, these functions are indispensable for rendering images and animations, as they help determine how objects rotate and move in a virtual space. The application of trigonometric functions extends beyond theoretical studies; they are used in practical situations as well. For instance, when constructing buildings or bridges, engineers must calculate angles and distances accurately. By employing trigonometric functions, they can ensure that their designs are both safe and efficient. Additionally, navigation systems, such as GPS, rely on trigonometric functions to pinpoint locations and calculate distances between points on Earth. This highlights the importance of these functions in everyday life and various industries. Furthermore, the concept of periodicity in trigonometric functions is significant in mathematics. Both the sine and cosine functions exhibit periodic behavior, meaning they repeat their values in regular intervals. This characteristic is crucial in modeling phenomena such as sound waves, light waves, and seasonal changes. The periodic nature of trigonometric functions allows mathematicians and scientists to predict future events based on past data, making them invaluable in research and analysis. In conclusion, trigonometric functions are not only foundational elements of mathematics but also powerful tools that facilitate understanding and solving complex problems across various disciplines. Their relevance in real-world applications underscores the need for students to grasp these concepts thoroughly. As we continue to explore the vast realms of science and technology, the importance of trigonometric functions will undoubtedly remain significant, shaping our understanding of the world around us.

三角函数在数学研究中是基础，特别是在几何和微积分领域。这些函数将三角形的角度与其边的长度联系起来，为解决科学和工程中的各种问题提供了基本工具。主要的三角函数包括正弦、余弦和正切，每个函数在不同的应用中都发挥着重要作用。例如，正弦函数用sin(x)表示，被定义为直角三角形中对边与斜边的比率。类似地，余弦函数用cos(x)表示，是邻边与斜边的比率。正切函数tan(x)则是正弦和余弦函数的比率，也可以表示为对边与邻边的比率。理解这些三角函数对物理、工程和计算机科学等领域的学生和专业人士至关重要。在物理学中，这些函数有助于描述振动运动、波动模式和圆周运动。工程师利用三角函数分析力量、设计结构，并创建模拟现实场景的模型。此外，在计算机图形学中，这些函数对于渲染图像和动画是不可或缺的，因为它们帮助确定对象在虚拟空间中的旋转和移动方式。三角函数的应用不仅限于理论研究；它们也用于实际情况。例如，在建造建筑物或桥梁时，工程师必须准确计算角度和距离。通过使用三角函数，他们可以确保设计既安全又高效。此外，导航系统，如GPS，依赖于三角函数来确定位置和计算地球上两点之间的距离。这突显了这些函数在日常生活和各个行业中的重要性。此外，三角函数中周期性的概念在数学中也很重要。正弦和余弦函数都表现出周期性行为，这意味着它们的值在规律的间隔内重复。这一特性在建模声音波、光波和季节变化等现象中至关重要。三角函数的周期性使得数学家和科学家能够基于过去的数据预测未来事件，从而使它们在研究和分析中变得不可或缺。总之，三角函数不仅是数学的基础元素，也是促进理解和解决各学科复杂问题的强大工具。它们在现实应用中的相关性强调了学生彻底掌握这些概念的必要性。随着我们继续探索科学和技术的广阔领域，三角函数的重要性无疑将保持显著，塑造我们对周围世界的理解。