12.1 导言:极地坐标和参数等量

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  导言:极地坐标和参数等量

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  In earlier mathematics, graphing took place in  the rectangular plane, also known as the Cartesian plane or the $\begin{array}{r}xy\end{array}$ -plane. The study of this plane has an impact on the understanding of points as they move from arbitrary space into specific locations. The rectangular plane is extremely useful in measurement and placement, and in understanding distance, length, area, and the attributes of functions.  
  ::在早期的数学中,在矩形平面(又称笛卡尔平面或X-平面)中进行了图形绘制,该平面的研究对从任意空间向特定地点移动的点的理解产生了影响。 矩形平面在测量和定位以及理解距离、长度、面积和功能属性方面非常有用。

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  We'll now begin to explore a new idea in which the graph is no longer rectangular but circular. This type of graphing is called "polar," where all points are graphed in relation to a "pole," and concentric circles represent placements along the graph. The pole is the center of the graph, representing the starting point for the graph.
  ::我们现在将开始探索一个新的想法, 即图形不再是矩形, 而是圆形。 这种类型的图形叫“ 极 ” , 所有点都用“ 极” 来图形, 和同心圆代表图的方位。 极是图的中心, 代表图的起点 。

  

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  The coordinates of the points in polar form no longer represent a horizontal and vertical place, but now denote the distance from the pole and the measure of the angle formed. We can convert rectangular coordinates to polar coordinates and plot equations on the polar grid as well. In this chapter, we'll explore the types of equations and their resultant graphs in the polar coordinate system.  
  ::极形点的坐标不再代表水平和垂直位置, 但现在表示离极的距离和角的度量。 我们可以将矩形坐标转换为极坐标和极网的绘图方程。 在本章中, 我们将探索极坐标系统中的方程类型及其产生的图形 。

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  In addition, we will determine how complex numbers are converted to polar form. There are also special formulas for finding the product, quotient, and powers of complex numbers in polar form. These formulas have applications within fractal geometry and in physics.
  ::此外,我们将确定如何将复杂数字转换成极形。还有以极形形式查找复杂数字的产品、商数和功率的特殊公式。这些公式在分形几何和物理学中都有应用。

  

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  Finally, this chapter will explore the modeling of movement through the use of parametric equations. Parameters are the independent variables in a set of equations that are being applied to situations like motion. While you may have already explored distance equals rate multiplied by time or  $\begin{array}{r}d=rt\end{array}$ , we need to add a third dimension to our description of motion: direction.
  ::最后,本章将探讨通过使用参数方程式进行移动的模型。参数是一系列正适用于运动等情况的方程式中独立的变量。虽然您可能已经探索过距离等于乘以时间或 d=rt的速度,但我们需要增加第三个维度来描述运动:方向。