law of cosines

简明释义

余弦定理

英英释义

例句

1.Architects often use the law of cosines 余弦定理 to calculate the lengths of structural components in non-right angled triangles.

建筑师经常使用law of cosines 余弦定理 来计算非直角三角形中结构组件的长度。

2.In physics, the law of cosines 余弦定理 helps in resolving vector components when forces are not acting at right angles.

在物理学中，law of cosines 余弦定理 有助于在力不垂直作用时分解向量分量。

3.When solving for an angle in a triangle, the law of cosines 余弦定理 can help determine the measure using the lengths of the sides.

在解三角形中的角时，law of cosines 余弦定理 可以利用边的长度来确定角度的大小。

4.The law of cosines 余弦定理 is particularly useful in navigation when calculating distances between points on a map.

在导航中，law of cosines 余弦定理 特别有用，可以计算地图上点与点之间的距离。

5.In a triangle where you know two sides and the included angle, you can apply the law of cosines 余弦定理 to find the third side.

在一个三角形中，如果你知道两条边和夹角，你可以使用law of cosines 余弦定理 来找到第三条边。

作文

The law of cosines is a fundamental principle in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. This theorem is particularly useful for solving triangles that are not right-angled, providing a way to calculate unknown side lengths or angles when certain other dimensions are known. The formula is expressed as: c² = a² + b² - 2ab * cos(C), where 'c' represents the length of the side opposite angle C, and 'a' and 'b' are the lengths of the other two sides. 余弦定理是三角学中的一个基本原理，它将三角形的边长与其中一个角的余弦相关联。这个定理在解决非直角三角形时尤其有用，当已知某些其他尺寸时，它提供了一种计算未知边长或角度的方法。该公式表达为：c² = a² + b² - 2ab * cos(C)，其中'c'表示对角C的边的长度，而'a'和'b'是另外两个边的长度。To understand the law of cosines, it is essential to visualize how it applies to different types of triangles. For instance, in an acute triangle, all angles are less than 90 degrees, and the sides can be calculated using the law of cosines if we know two sides and the included angle. Conversely, in an obtuse triangle, where one angle is greater than 90 degrees, the same law still holds true, allowing us to find missing lengths or angles. This versatility makes the law of cosines a powerful tool in various fields such as architecture, engineering, and physics.In practical applications, the law of cosines can be used to determine distances between points in navigation or to calculate forces in physics problems. For example, if two ships are sailing towards each other from different ports, knowing their respective distances from a common point and the angle between their paths allows one to use the law of cosines to find the distance between them. This calculation is crucial for safe navigation and planning.Moreover, the law of cosines is often introduced in geometry classes as a natural extension of the Pythagorean theorem. While the Pythagorean theorem only applies to right triangles, the law of cosines generalizes this concept to all triangles. This connection helps students appreciate the broader applications of trigonometric principles and encourages deeper learning in mathematics.In conclusion, the law of cosines is an essential theorem in trigonometry that provides valuable insights into the relationships between the sides and angles of triangles. Its ability to apply to various types of triangles makes it a versatile tool in mathematical problem-solving. Understanding the law of cosines not only enhances one's skills in geometry but also opens up opportunities for practical applications in real-world situations. As students continue to explore trigonometry, mastering the law of cosines will undoubtedly serve them well in their academic and professional endeavors.

余弦定理是三角学中的一个基本原理，它将三角形的边长与其中一个角的余弦相关联。这个定理在解决非直角三角形时尤其有用，当已知某些其他尺寸时，它提供了一种计算未知边长或角度的方法。该公式表达为：c² = a² + b² - 2ab * cos(C)，其中'c'表示对角C的边的长度，而'a'和'b'是另外两个边的长度。要理解余弦定理，首先需要想象它如何应用于不同类型的三角形。例如，在锐角三角形中，所有角都小于90度，如果我们知道两条边和夹角，就可以使用余弦定理来计算。而在钝角三角形中，其中一个角大于90度，同样适用余弦定理，可以找出缺失的边长或角度。这种灵活性使得余弦定理在建筑、工程和物理等多个领域成为一种强大的工具。在实际应用中，余弦定理可以用于确定导航中点与点之间的距离，或者在物理问题中计算力。例如，如果两艘船从不同的港口向彼此航行，知道它们各自距离共同点的距离和航线之间的角度，就可以使用余弦定理来找到它们之间的距离。这个计算对于安全导航和规划至关重要。此外，余弦定理通常在几何课上作为毕达哥拉斯定理的自然延伸介绍。虽然毕达哥拉斯定理仅适用于直角三角形，但余弦定理将这一概念推广到所有三角形。这种联系帮助学生欣赏三角学原理的更广泛应用，并鼓励他们在数学中深入学习。总之，余弦定理是三角学中的一个重要定理，为三角形的边和角之间的关系提供了宝贵的见解。它适用于各种类型的三角形，使其成为数学问题解决中的多功能工具。理解余弦定理不仅提高了几何技能，还为实际应用打开了机会。在学生继续探索三角学的过程中，掌握余弦定理无疑将对他们的学术和职业发展大有裨益。