radians

简明释义

英[ˈreɪdiənz]美[ˈreɪdiənz]

n. [数]弧度（radian 的复数）

英英释义

单词用法

同义词

反义词

例句

1.Not greatly complicated really; just remember that that the cone's inner and outer angles are specified in radians not degrees.

并不是很复杂。只要记好锥形的内外角是用弧度而不是角度表示的。

2.360 radians per second.

360弧度每秒。

3.Many spatial distance algorithms require the Numbers to be in radians, while others can work with degrees.

许多空间距离算法要求采用以弧度表示的数据，而其他算法则要求使用以度表示的数据。

4.It is feel pretty and magnificent, and it has a lot of radians.

到现场看到它还觉得挺壮丽的，而且他有很多弧度一节一节的。

5.How many meters per second is linear, as opposed to how many radians per second, which is angular velocity.

每秒走过多少米就是线速度，和每秒经过多少弧度是相反的，那是角速度。

6.That's our definition of radians.

这是对于弧度的定义。

7.It seemed that segments must be short enough so that any curve that developed would be well defined, i. e., there should be some maximum Angle between adjacent segments, perhaps 0.1 radians.

它看来，部分必须太长，从而使任何曲线，发达国家将是很好的界定，也就是说，应该有一些最大角相邻部分，也许0.1弧度。

8.In trigonometry, angles can be measured in degrees or radians (弧度).

在三角学中，角度可以用度数或弧度（弧度）来衡量。

9.To find the length of an arc, you can use the formula: length = radius × angle in radians. (弧度)

要找到弧的长度，可以使用公式：长度 = 半径 × 角度（以弧度表示）。(弧度)

10.The formula for converting degrees to radians is to multiply by π/180. (弧度)

将度数转换为弧度的公式是乘以π/180。(弧度)

11.A full circle is equal to 2π radians. (弧度)

一个完整的圆等于2π弧度。（弧度）

12.In calculus, we often use radians (弧度) for the derivatives of trigonometric functions.

在微积分中，我们通常使用弧度（弧度）来计算三角函数的导数。

作文

In mathematics, particularly in the field of trigonometry, the concept of radians (弧度) plays a crucial role in understanding angles and their measurements. Unlike degrees, which are a more familiar way to measure angles, radians provide a natural way to relate angular measurement to the arc length on a circle. One radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. This definition not only simplifies many mathematical formulas but also enhances our comprehension of circular motion and periodic functions.To illustrate the importance of radians (弧度), consider the unit circle, which is a circle with a radius of one centered at the origin of a coordinate plane. In this context, the angle in radians corresponds directly to the length of the arc that the angle subtends. For example, a quarter turn around the circle, or 90 degrees, corresponds to a radian measure of π/2. This direct relationship makes it easier to perform calculations involving sine, cosine, and tangent functions, which are foundational in trigonometry.Moreover, radians (弧度) are essential in calculus, particularly when dealing with derivatives and integrals of trigonometric functions. When angles are measured in radians, the derivatives of sine and cosine functions take on simpler forms: the derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x). This simplicity is lost when using degrees, making radians the preferred unit in higher mathematics.Another significant aspect of radians (弧度) is their role in physics, especially in the study of oscillations and waves. When analyzing harmonic motion, such as the swinging of a pendulum or the vibrations of a guitar string, angles are often expressed in radians. This is because the equations governing these motions, such as those derived from Hooke's Law, inherently involve angular measurements that are most naturally expressed in radians. Thus, using radians (弧度) allows for a more intuitive understanding of these phenomena.In conclusion, mastering the concept of radians (弧度) is vital for anyone studying mathematics, physics, or engineering. Their unique properties facilitate a deeper understanding of angular relationships and simplify complex calculations. As we advance in our studies, we find that radians are not just a mathematical curiosity but a fundamental tool that bridges various fields of science and mathematics. Embracing radians will undoubtedly enhance our analytical skills and enrich our understanding of the world around us.

在数学中，特别是在三角学领域，radians（弧度）的概念在理解角度及其测量方面发挥着至关重要的作用。与度数不同，度数是一种更为熟悉的角度测量方式，而radians则提供了一种自然的方式，将角度测量与圆上的弧长联系起来。一个radian被定义为在圆心处由与圆的半径相等的弧所形成的角度。这一定义不仅简化了许多数学公式，还增强了我们对圆周运动和周期函数的理解。为了说明radians（弧度）的重要性，可以考虑单位圆，这是一个半径为1并位于坐标平面原点的圆。在这个背景下，以radians表示的角度与该角度所对应的弧长直接相关。例如，圆周的四分之一转动，即90度，对应于radian的测量为π/2。这种直接关系使得涉及正弦、余弦和正切函数的计算变得更加简单，这些函数是三角学的基础。此外，radians（弧度）在微积分中至关重要，尤其是在处理三角函数的导数和积分时。当角度以radians表示时，正弦和余弦函数的导数呈现出更简单的形式：sin(x)的导数是cos(x)，而cos(x)的导数是-sin(x)。这种简单性在使用度数时会消失，因此在更高层次的数学中，radians成为首选单位。radians（弧度）的另一个重要方面是它们在物理学中的作用，特别是在研究振动和波动时。当分析谐波运动，如摆的摆动或吉他弦的振动时，角度通常以radians表示。这是因为支配这些运动的方程，例如由胡克定律推导出的方程，固有地涉及以radians表示的角度测量。因此，使用radians（弧度）可以更直观地理解这些现象。总之，掌握radians（弧度）的概念对于任何学习数学、物理或工程的人来说都是至关重要的。它们独特的属性促进了对角度关系的更深入理解，并简化了复杂的计算。随着我们学习的深入，我们发现radians不仅仅是一个数学好奇心，而是一个桥接科学和数学各个领域的基本工具。接受radians无疑会增强我们的分析能力，并丰富我们对周围世界的理解。