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.
angle is in standard position 角的标准位置
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.
Positive and negative angles角的正负
Positive angles are generated by counterclockwise rotation, and
negative angles by clockwise rotation.
note that angles a and b have the same initial and
terminal sides. Such angles are coterminal.
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.
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.
To define a radian, you can use a central angle of a circle, one whose vertex is the center of the circle.
Arc length = radius when q = 1 radian
These and other common angles are shown in the figure
Example 1 Convert from degrees to radians
Example 2 Convert from radians to degrees