國際課程提前學，A-Level數學之三角函數1：角的測量

Angles角An angle is determined by a rotation of a ray about its endpoint. The endpoint of the ray is the vertex of the angle. The stating position of the ray is the initial side of the angle, and the position after rotation is the terminal side.

角度是由一條射線繞著頂點旋轉構成的，射線的端點是角的頂點，和起始邊與終邊一起構成了一個角。

angle is in standard position 角的標準位置

This perception of an angle fits a coordinate system in which the origin
is the vertex and the initial side coincides with the positive x-axis.
Such an angle is in standard position.
角的標準位置，頂點在直角坐標系原點，初始邊與x軸的正半軸重合。

Positive and negative angles角的正負

Positive angles are generated by counterclockwise rotation, and
negative angles by clockwise rotation.
正角是逆時針旋轉形成的角，負角是順時針旋轉形成的角。
Coterminal 終邊相同的角
note that angles a?and b?have the same initial and
terminal sides. Such angles are coterminal.
a和b角有相同的初始邊和終邊，這樣特點的角是終邊相同的角。
?Degree angles角的測量（度數）

A way to measure angles is in terms of degrees, denoted by the symbol °.
A measure of one degree (1°) is equivalent to a rotation of a complete revolution about the vertex.
角的大小可以用度數測量，一個完整圓周是360度。
?Radian Measure 角的測量（弧度）

he second way of measure of an angle is determined by the amount of rotation from the initial side to the terminal side，this way to measure angles is in radians. This type of measure is especially useful in calculus.
第二個測量角度的方法是用弧度
To define a radian, you can use a central angle of a circle, one whose vertex is the center of the circle.
圓心在原點的圓心角用來測量弧度的大小。

Arc length = radius when q??= 1 radian
?
當弧線等于圓的半徑時，弧度等于1.
?常見的角度弧度
These and other common angles are shown in the figure
?

Example 1

Convert from degrees to radians
例題：轉化角度到弧度

Example 2

Convert from radians to degrees
例題：轉化弧度到角度