sine formula

简明释义

正弦公式

英英释义

例句

1.When studying waves, the sine formula 正弦公式 helps in understanding their properties.

在研究波动时，sine formula 正弦公式 有助于理解它们的性质。

2.The sine formula 正弦公式 states that the ratio of the length of a side to the sine of its opposite angle is constant.

sine formula 正弦公式 表明边长与其对角的正弦比是恒定的。

3.To find the area of a triangle, we can use the sine formula 正弦公式 to calculate it efficiently.

为了找到一个三角形的面积，我们可以使用 sine formula 正弦公式 来高效计算。

4.Using the sine formula 正弦公式, we can determine the height of a building from a distance.

利用 sine formula 正弦公式，我们可以从远处确定一座建筑的高度。

5.In trigonometry, the sine formula 正弦公式 is essential for solving triangles.

在三角学中，sine formula 正弦公式 对于解决三角形是必不可少的。

作文

In the study of trigonometry, one of the most essential tools is the sine formula. This formula relates the angles and sides of a triangle, particularly in the context of non-right triangles. The sine formula states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles in the triangle. Specifically, it can be expressed as: a/sin(A) = b/sin(B) = c/sin(C), where 'a', 'b', and 'c' are the lengths of the sides, and 'A', 'B', and 'C' are the respective opposite angles. Understanding this relationship is crucial for solving various problems in geometry and physics.The significance of the sine formula extends beyond mere academic interest; it has practical applications in fields such as engineering, architecture, and even computer graphics. For instance, in engineering, when designing structures, engineers must often calculate forces acting on different components, which requires a solid grasp of trigonometric principles, including the sine formula. Similarly, architects use these calculations to ensure that buildings are both aesthetically pleasing and structurally sound.Moreover, the sine formula plays a vital role in navigation and astronomy. Sailors and pilots rely on trigonometric calculations to determine their position relative to the Earth’s surface. By using the sine formula, they can accurately compute distances and angles, ensuring safe passage across vast oceans or through the skies.In addition to its practical uses, the sine formula also serves as a gateway to more advanced mathematical concepts. For students, mastering the sine formula can lead to a deeper understanding of calculus and analytical geometry. It introduces them to the idea of functions and their properties, laying the groundwork for exploring topics like wave functions and oscillations in physics.Furthermore, the sine formula is not just limited to triangles; it can also be used in conjunction with other trigonometric identities to solve complex equations. For example, when paired with the cosine and tangent formulas, students can tackle a wide range of problems, from simple triangle calculations to more complicated scenarios involving circular motion.In conclusion, the sine formula is a fundamental concept in mathematics that has far-reaching implications in various disciplines. Its ability to relate angles and sides of triangles makes it an invaluable tool for students, professionals, and anyone involved in fields that require spatial reasoning. Grasping the sine formula opens up a world of possibilities, allowing individuals to solve problems that involve not only geometry but also real-world applications in science and engineering. Therefore, a thorough understanding of the sine formula is essential for anyone looking to excel in mathematics or related fields.

在三角学的研究中，最基本的工具之一就是sine formula。这个公式涉及到三角形的角和边，特别是在非直角三角形的背景下。sine formula指出，三角形一边的长度与其对角的正弦的比率在三角形的所有三条边和角中是恒定的。具体来说，可以表示为：a/sin(A) = b/sin(B) = c/sin(C)，其中'a'、'b'和'c'是边的长度，而'A'、'B'和'C'是各自的对角。理解这种关系对于解决几何和物理中的各种问题至关重要。sine formula的重要性不仅限于学术兴趣；它在工程、建筑甚至计算机图形学等领域具有实际应用。例如，在工程中，设计结构时，工程师必须计算作用于不同组件的力，这需要对三角学原理有扎实的掌握，包括sine formula。同样，建筑师使用这些计算来确保建筑既美观又结构稳固。此外，sine formula在导航和天文学中也发挥着至关重要的作用。水手和飞行员依赖三角计算来确定他们相对于地球表面的位置信息。通过使用sine formula，他们可以准确计算距离和角度，确保在广阔的海洋或天空中的安全通行。除了实际用途外，sine formula还是更高级数学概念的入门。对于学生来说，掌握sine formula可以加深他们对微积分和解析几何的理解。它向他们介绍了函数及其属性的概念，为探索波函数和物理中的振动等主题奠定基础。此外，sine formula不仅限于三角形；它还可以与其他三角恒等式结合使用，以解决复杂的方程。例如，当与余弦和正切公式配对时，学生可以处理从简单三角形计算到涉及圆周运动的更复杂场景的广泛问题。总之，sine formula是数学中的一个基本概念，在各个学科中具有深远的影响。它将三角形的角和边联系起来，使其成为学生、专业人士以及任何涉及空间推理领域的人的宝贵工具。掌握sine formula开启了一个可能性的大门，使个人能够解决不仅涉及几何的问题，还包括科学和工程中的实际应用。因此，深入理解sine formula对于任何希望在数学或相关领域中脱颖而出的人来说都是至关重要的。