And so you can express derivatives either in terms of x y or in terms of r and theta with simple relations between them .

表示它的微分，要么用x和y，要么用r和 θ，它们之间有简单的关系。

It is d theta dt if you want . Well what is the kinetic energy now ?

也就是d θ /dt，现在动能是什么？

And differentiate the right-hand side as a function of b and theta .

把右边当成b和 θ的函数 来 做 微分。

It is clearly a simple harmonic oscillation in theta because this is a constant .

很明显，这是关于， θ的简谐振荡，因为这是不变的。

I want to put r and theta in there .

我想把r和 θ放进去。

On what else do you use theta for if not angles ?

如果不用 angles的话，你会用些什么 词去 描述角度呢？

Let 's start with a simple example of an incline at an angle theta .

让我们以一个角度为， θ的斜坡为例。

That 's really the same thing except now are variables are a b and theta .

除了变量变成了a，b和 θ之外，其他事情完全相同。

The next states theta brainwaves are typically of even greater amplitude and slower frequency .

下一个状态时 θ脑电波，代表更大的振幅和更小的频率。

You pick up any theta beta rushes last night ?

你昨天晚上有没有接 姐妹会的人？

Well you could call that the rate of change of theta with respect to theta with a constant .

你可以称之为，保持a不变， θ关于θ自身的变化率。

We want to set up the bounds for rho for a given phi and theta .

给定φ和 θ，要知道ρ的范围。

The goal is to see how things change when I change theta by a little bit .

我们的目标是来看看当我稍微改变 θ 时 将会怎样变化。

NdS Well you could parametize a sphere in terms of phi and theta .

是用dφdθ表示的。，We，know，what，n，dS，are，in，terms，of，d，phi，，d， theta。，你可以用φ和θ，将球面参数化。

Db And we can solve for db in terms of d theta .

我们求解出了用d θ 来 表示的。

Then when I change theta there 's two options .

那么，当我改变 θ时，会有两个选择。

See this is the same formula as the one over there just dividing everything by partial theta and with subscripts little a.

这和那边的公式是一样的，只是通过偏 θ和下标a把所有的事情分开，如果对你来说用这种方法更容易理解。

Well now that it 's only a function of a and theta I know what it means to take the partial derivative with respect to theta keeping a constant . I know how to do it .

现在它成了一个只关于a和 θ的函数，我知道保持a恒定不变，关于θ的偏导数是什么，我知道这怎么做。

When the frictional force and mg sine theta are exactly equal .

当摩擦力和mgsin θ，完全相等的时候。

R I want to see a theta . I don 't want to see an R.

我希望能看到 θ，而不希望看到。

So actually as a function of b and theta it 's given over there .

在那边已经给出了关于b和 θ的函数。

X y But we can also switch from r theta to xy .

也可把r， θ转换为。

For example on spheres we typically integrate with respect to phi and theta for latitude and longitude angles .

例如在球面上，我们通常，对纬度 角φ和经度角 θ 做积分。

Well I would use phi and theta as my coordinates .

需要以φ和 θ为坐标。

And then because theta and b change that causes the area to change .

因为 θ和b变化，这导致面积改变。

One is I keep a constant and then of course b will have to change because if this width stays the same then when I change theta the height increases and then this side length increases .

一个是我保持a恒定，那么当然b就会变化，因为这个宽是不变的。，那么当改变 θ 角时，高度增加了，从而这条边的长度增加了。

This is a small-angle approximation ; it 's a very good approximation and theta is in radians .

这是小角度近似值；，它是个很好的近似值， θ是弧度。