Trigonometry 三角学.ppt

第五章
Trigonometry 三角
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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。
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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 plete revolution contains 360°,which is 2π rad.
Therefore,
1 rad = (180/π)°≈ °
1°= (π/180) rad ≈ rad
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The following table gives the correspondence between degree and radian measures of mon 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
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二、Angle in Standard Position 角的标准坐标位置
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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.
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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 positi