trigonometrical function

简明释义

三角函数

英英释义

例句

1.The unit circle is a fundamental concept for understanding trigonometrical functions 三角函数.

单位圆是理解三角函数的基本概念。

2.In calculus, we often use the trigonometrical function 三角函数 to solve problems related to angles and distances.

在微积分中，我们常常使用三角函数来解决与角度和距离相关的问题。

3.The sine and cosine are two of the most important trigonometrical functions 三角函数 in mathematics.

正弦和余弦是数学中最重要的两个三角函数。

4.To find the height of a building, you can use a trigonometrical function 三角函数 based on the angle of elevation.

要找出建筑物的高度，可以根据仰角使用三角函数。

5.Engineers often apply trigonometrical functions 三角函数 to calculate forces in structures.

工程师经常应用三角函数来计算结构中的力。

作文

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. One of the most important concepts in trigonometry is the trigonometrical function, which helps us understand these relationships in a systematic way. The primary trigonometrical functions include sine, cosine, and tangent, each corresponding to specific ratios of a right triangle's sides. For example, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Similarly, cosine represents the ratio of the adjacent side to the hypotenuse, while tangent is the ratio of the opposite side to the adjacent side.Understanding trigonometrical functions is crucial not only in pure mathematics but also in various applications across different fields. In physics, for instance, trigonometrical functions are used to model periodic phenomena such as sound waves and light waves. Engineers utilize these functions to analyze forces and design structures, ensuring that they can withstand various stressors.Moreover, trigonometrical functions play a vital role in computer graphics. When rendering images, it is essential to calculate angles and distances accurately, which often involves the use of sine and cosine functions. This application highlights how fundamental mathematical principles can translate into practical technology.In addition to their practical applications, trigonometrical functions also have a rich theoretical background. They are interconnected through various identities, such as the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1 for any angle θ. These identities allow mathematicians to simplify expressions and solve complex equations involving angles.Learning about trigonometrical functions also enhances our problem-solving skills. For instance, when faced with a real-world problem involving heights and distances, we can apply these functions to find unknown values through triangulation. This method has been used historically in navigation, surveying, and even astronomy.In conclusion, the study of trigonometrical functions is essential for anyone pursuing a career in science, technology, engineering, or mathematics (STEM). Their applications are vast and varied, spanning from theoretical mathematics to practical engineering and computer graphics. By mastering these functions, we not only gain a deeper understanding of geometry and angles but also equip ourselves with valuable tools for solving real-world problems. As we continue to explore the intricacies of mathematics, the significance of trigonometrical functions remains ever-present, illustrating the beauty and utility of this fascinating field of study.

三角学是数学的一个分支，研究三角形的角和边之间的关系。在三角学中，一个非常重要的概念是三角函数，它帮助我们系统地理解这些关系。主要的三角函数包括正弦、余弦和正切，每个函数都对应于直角三角形边的特定比率。例如，某个角的正弦定义为对边长度与斜边长度的比率。类似地，余弦代表邻边与斜边的比率，而正切则是对边与邻边的比率。理解三角函数不仅在纯数学中至关重要，而且在各个领域的应用中也发挥着重要作用。例如，在物理学中，三角函数用于建模周期现象，如声波和光波。工程师利用这些函数来分析力并设计结构，以确保它们能够承受各种压力。此外，三角函数在计算机图形学中也发挥着重要作用。在渲染图像时，准确计算角度和距离是至关重要的，这通常涉及到正弦和余弦函数的使用。这一应用突显了基本数学原理如何转化为实用技术。除了它们的实际应用，三角函数还有丰富的理论背景。它们通过各种恒等式相互联系，例如毕达哥拉斯恒等式，指出对于任何角θ，sin²(θ) + cos²(θ) = 1。这些恒等式使数学家能够简化表达式并解决涉及角的复杂方程。学习三角函数还增强了我们的解决问题的能力。例如，当面对涉及高度和距离的现实问题时，我们可以应用这些函数通过三角测量找到未知值。这种方法在历史上被用于导航、测量甚至天文学。总之，学习三角函数对任何追求科学、技术、工程或数学（STEM）职业的人来说都是必不可少的。它们的应用广泛而多样，从理论数学到实用工程和计算机图形学。通过掌握这些函数，我们不仅深入理解几何和角度，还为解决现实问题提供了宝贵的工具。在继续探索数学的复杂性时，三角函数的重要性始终存在，展示了这个迷人领域的美丽和实用性。