Coursework 代写:弧度测量

2017-02-01 14:58

弧度是角的测量单位，并已应用在许多数学领域。一弧度的角，在一个单位圆的弧长的中心，1是平等的。作为一个单位圆周长等于2π，圆等于2π。这里π是一个数学常数，约等于3.1415926。正式的，π是圆的周长与其直径的比值。图3显示了由一个单位圆弧度的定
弧度是由18世纪数学家发明的，所以它比度较短的历史。最初的动机是数学家要合理地测量角度，而不是选择任意数量如360。他们发现，一个圆的周长与其直径的比值是一个常数，用希腊字母π代表。然后一个完整的圆圈被定义为2π弧度。弧度的定义是美丽的，但它的计算π非常具有挑战性的，因为它不能准确表达为两个整数比。历史上，人们花费大量的经验来计算它的近似值。多亏了电脑，这项工作现在变得很简单了

Coursework 代写:弧度测量

Radian is the SI unit for angle measure, and it has been used in many mathematical fields. One radian is the angle subtended at the center of a unit circle by an arc that is equal in length to 1. As the circumference of a unit circle is equal to 2π, a full circle is equal to 2π. Here π is a mathematical constant and is approximately equal to 3.1415926. Formally, π is the ratio of a circle's circumference to its diameter. Figure 3 shows the definition of radian by a unit circle.

Radian is invented by mathematicians in the 1700s, so it has a much shorter history than degree. The original motivation is that mathematicians want to measure angles rationally rather than choosing an arbitrary number like 360. They find that the ratio of a circle’s circumference to its diameter is a constant, represented by the Greek letter π. Then a full circle is defined as 2π radians. The definition of radian is beautiful, but it’s very challenging to compute π, because it cannot be expressed exactly as a ratio of two integers. Historically, people spend a lot of experience to calculate its approximate value. Thanks to the computer, this work has become very simple now.