5.8:摘要:角

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• 选择节摘要:角

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  摘要:角

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  Chapter Summary
  ::章次摘要

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  The study of trigonometry can be summarized by analyzing the roots of the very word:
  ::三角测量研究可以通过分析这个词本身的根源来总结:

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  "tri" is the prefix meaning  three,
  ::"三"是前缀的意思是三

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  "gonia" is a root meaning  angle, and
  ::"Gonia"是一个根含义角度,

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  "metry" is from the Greek word  metron,  meaning  to measure.
  ::"测量"来自希腊语的节拍器, 意思是测量。

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  Trigonometry is the measuring of angles in three-sided figures. In this chapter we have learned many tools to understand how to measure angles.
  ::三角测量是三面数字角度的测量。 在本章中,我们学到了许多工具来理解如何测量角度。

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  In this chapter, we learned:
  ::在本章中,我们学到:

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  • Angles in standard position have their initial side on the positive  $\begin{array}{r}x-\end{array}$ axis . 
    ::处于标准位置的角在正 X - 轴上有其初始侧面。
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  • Coterminal angles are angles that can be represented in many ways, but are equivalent angles because they have the same initial side and terminal side. 
    ::直角是可以用多种方式表示的角,但却是等角,因为它们有相同的初始侧面和末端面。
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  • The conversion factor to convert from degrees to radians is  $\begin{array}{r}\frac{\pi }{{180}^{\circ }}.\end{array}$  
    ::从度向弧度转换为弧度的转换系数为 180 。
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  • The length of any arc is  $\begin{array}{r}s=r\theta ,\end{array}$  where  $\begin{array}{r}s\end{array}$  is the length of the arc,  $\begin{array}{r}r\end{array}$  is the radius, and  $\begin{array}{r}\theta \end{array}$  is the measure of the angle in radians.
    ::任何弧的长度为 s=r, 其中 s 是弧的长度, r 是半径, 是角以弧度的量度 。
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  • The area of a sector is  $\begin{array}{r}A=\frac{1}{2}{r}^2\theta ,\end{array}$  where  $\begin{array}{r}\theta \end{array}$  is in radians.
    ::一个扇区的区域为A=12r2,其中为弧度。
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  • Angular speed is   $\begin{array}{r}\omega =\frac{\theta }{t},\end{array}$  where omega  $\begin{array}{r}\omega \end{array}$   is the symbol for angular speed ,   $\begin{array}{r}\theta \end{array}$   is the angle of rotation expressed in radians, and   $\begin{array}{r}t\end{array}$   is the time to complete the rotation.
    ::角速度为 t, 角速度的符号是 omega , 是 角速度的符号, 是以弧度表示的旋转角度, t 是 完成旋转的时间 。
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  • Linear speed is  $\begin{array}{r}v=r\omega ,\end{array}$  where  $\begin{array}{r}v\end{array}$  is the linear speed ,  $\begin{array}{r}r\end{array}$  is the radius, and  $\begin{array}{r}\omega \end{array}$  is the  angular speed.
    ::线性速度是 v=r, 其中 v 是线性速度, r 是半径, r 是角速度 。

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  Chapter Review 
  ::回顾章次审查

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  Try the following cumulative review problems to practice the concepts studied in this chapter:
  ::尝试下列累积审查问题,以实践本章所研究的概念: