You already know that angles are measured by degrees (360° is a complete revolution). An alternative method is based on the circumference of a circle.
你已经知道，角度是用度数来衡量的（360°是一个完整的旋转）。另一种方法是基于圆的周长。
If an arc of a circle is drawn such that it is the same length as the radius, then the angle created is called one radian (1C), as shown below.
如果画一个圆弧，使其长度与半径相同，那么所形成的角度就称为一弧度（1C），如下图所示。
From the diagram you can see that dividing the circumference by the radius will give the number of radians in one complete revolution. Therefore, the number of radians in one revolution is,
从图中你可以看到，用圆周率除以半径就可以得到一个完整的旋转的弧度数。因此，一圈的弧度数是，
These basic conversions are useful to know 这些基本的转换是很有用的，要知道:
Fractions of 180° can be written in radians by using 180° = π rad
180°的分数可以用弧度来写，即180°=π rad
For example:
You also need to be able to convert an angle given in radians to degrees 你还需要能够将以弧度给出的角度转换为度数:
For example:
This means that one radian is just a little less than 60°.
这意味着，一个弧度只比60°少一点。
Arc length and Area of a sector 弧长和扇形的面积Arc length 弧长
In the diagram below we can see that for a given angle θ, the length of the arc is rθ. (See if you can calculate this using the fact that the arc is θ/2π of the whole circumference.)
在下图中，我们可以看到，对于一个给定的角度θ，弧的长度是rθ。(看看你是否能用弧线是整个圆周的θ/2π这一事实来计算）。
Area of a sector 扇形的面积
Using the same idea, we find that the area of a sector of a circle is ½ r²θ.
用同样的思路，我们发现圆的一个扇形的面积是 ½ r²θ。
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