文档介绍：尽管三角学在ACT数学考试中所占比例不足7%，只有4或5道题，但这个知识点涉及面却很广。ACT数学考试试题可能会来自下列知识点中的一个。
① Angles 角；
② Trigonometric Functions 三角函数；
③ Trigonometric Identities 三角恒等式；
④ Graphs of Trigonometric Functions 三角函数图像；
⑤ Right Triangle Trigonometry 直角三角函数；
⑥ Triangle Problems 三角形问题。
第一节 Angles 角
一、 Radians 弧度
Angles can be measures in degrees or in radians (abbreviated as “rad”). The angle given by a complete revolution contains 360°,which is 2π rad.
Therefore,
1 rad = (180/π)°≈ °
1°= (π/180) rad ≈ rad
The following table gives the correspondence between degree and radian measures of some common angles
Degrees
0°
30°
45°
60°
90°
120°
135°
150°
180°
270°
360°
Radians
0
π/6
π/4
π/3
π/2
2π/3
3π/4
5π/6
π
3π/2
2π
二、Angle in Standard Position 角的标准坐标位置
The standard position of an angle occurs when we place its vertex at the origin of a coordinate system and its initial side on the positive x-axis.
The quadrant that contains the terminal side determines the quadrant that the angle lies in.
In the figure above, α represents an angle in Quadrant I, while β is in Quadrant III.
A positive angle is obtained by rotating the initial side counterclockwise until it coincides with the terminal side. Likewise, negative angles are obtained by clockwise rotation.
In the figure above, α is positive, while β is negative.
If the terminal side of an angle in standard position is one of the axes, the angle is a quadrant angle.
For example, 90°(π/2) and -180°(-π) are quadrant angles.
Every angle in standard position has a reference angle, which is the positive acute angle formed by the terminal side of the given angle and the x-axis. See examples below.
第二节 Trigonometric Functions 三角函数
For a general angle θ in standard position, we let P (x, y) be any point on the terminal side of θ and let r be the distance |OP| as shown in the figure above. Then we define the following trigonometric functions:
sin θ=y/r csc θ=r/y
cos θ=x/r sec θ=r/x
tan θ=