satisfies the condition tan is Ay over Ax..

满足其正切等于 Ay 除以 Ax
What this means--Now here's the main point.

这样的意义何在呢下面我要讲出重点
If you give me a pair of numbers, Ax and Ay,

如果给我一组数字 Ax 和 Ay
that's as good as giving me this arrow,

就相当于给了我这个箭头示意图
because I can find the length of the arrow by Pythagoras' theorem.

因为我可以利用毕达哥拉斯定理定理求出模长
And I can find the orientation of the arrow

我也可以求得矢量的方向
by saying the angle θ that satisfies tan is Ay over Ax.

通过求出满足正切等于 Ay 除以 Ax 的 θ角
You have the option of either working with

你可以选择使用
the two components of A or with the arrow.

A 的两个分量或者矢量图来计算
In practice,

在实际过程中
most of the time we work with these two numbers, Ax and Ay.

大多数时间我们就用 Ax 和 Ay 来计算
If you are describing a particle with location R,

如果你要描述一个位移为 R 的质点