The concept of angle is one of the most important concepts in geometry. The concepts of equality, sums, and differences of angles are important and used throughout geometry, but the subject of trigonometry is based on the measurement of angles.
There are two commonly used units of measurement for angles. The more familiar unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°. For the time being, we'll only consider angles between 0° and 360°, but later, in the section on trigonometric functions, we'll consider angles greater than 360° and negative angles.
Degrees may be further divided into minutes and seconds, but that division is not as universal as it used to be. Parts of a degree are now frequently referred to decimally. For instance seven and a half degrees is now usually written 7.5°. Each degree is divided into 60 equal parts called minutes. So seven and a half degrees can be called 7 degrees and 30 minutes, written 7° 30'. Each minute is further divided into 60 equal parts called seconds, and, for instance, 2 degrees 5 minutes 30 seconds is written 2° 5' 30". The division of degrees into minutes and seconds of angle is analogous to the division of hours into minutes and seconds of time.
Usually when a single angle is drawn on a xy-plane for analysis, we'll draw it with the vertex at the origin (0,0), one side of the angle along the x-axis, and the other side above the x-axis.
The other common measurement for angles is radians. For this measurement, consider the unit circle (a circle of radius 1) whose center is the vertex of the angle in question. Then the angle cuts off an arc of the circle, and the length of that arc is the radian measure of the angle. It is easy to convert between degree measurement and radian measurement. The circumference of the entire circle is 2 ( is about 3.14159), so it follows that 360° equals 2 radians. Hence, 1° equals /180 radians, and 1 radian equals 180/ degrees.
Most calculators can be set to use angles measured with either degrees or radians. Be sure you know what mode your calculator is using.
在几何学中,角是两条有公共端点的射线组成.这两条射线叫做角的边,它们的公共端点叫做角的顶点.角是用来测量两条有公共端点的射线的坡度差的.几何之父欧几里得曾定义角为在平面中两条不平行的直线的相对斜度.角在几何学和三角学中有着广泛的应用.角通常用三个字母表示：两条边上的点的字母写在两旁,顶点上的字母写在中间.
以角的端点为圆心做圆.由于圆的半径和周长成正比,而角是长度的比例,所以圆的大小不会影响角的测量.
弧度：用角在圆上所切出的圆弧的长度除以圆的半径,一般记作rad.弧度是国际单位制中规定的角的度量,但却不是中国法定计量单位,角度则是角在中国的法定计量单位.此外,弧度在数学及三角学中有广泛的应用.
角度：由角在圆上所切出的圆弧的长度除以圆的周长再乘以360的结果,一般用°来标记,读作“度”.一度可以继续分为60“分”或3600“秒”.角度在天文学和全球定位系统中有重要应用.
