A change from alpha wave drowsiness to lower frequency theta brain waves signify early sleep.

从α波睡意到较低频率的脑电波的变化表示早睡。

So this is going to be equal to the sine of theta.

可乘重力的大小。

So this is 90 minus theta degrees.

这个也是90-θ度。

There are three frequencies that we need to understand, Beta frequency, Theta frequency, and Alpha frequency.

我们需要理解三种频率，贝塔频率，西塔频率和阿尔法频率。

This is equal to the sine of theta.

可乘重力的大小。

So the factor by which the slice gets squished down in this direction is exactly cosine of theta.

因，切片 在这个方向上被压扁的因素正是 theta 的余弦。

This too will be 90 minus theta degrees.

再看如何求出这个角。

And that's why it's cosine of theta.

因 相等。

This right here is 90 minus theta.

那么上面这个角是多少。

So, the cosine of theta is equal to the (ball’s position) divided by its (amplitude).

因， theta 的余弦等于（球的位置）除它的（振幅）。

And so let's watch the animation before we get to the sine of theta.

我们在讲到正弦theta之前，先来看一下动画。

Theta waves occur if the brain is awake but relaxed, on autopilot or daydreaming.

Theta波在大脑清醒但放松、处于自动导航状态或白日梦出现。

I'm gonna use sine of theta, oh sorry, sine of phi.

我要使用正弦 theta， 哦抱歉，正弦 phi。

And now for the Y direction we can use the definition of sine of theta.

现在对于 Y 方向，我们可使用正弦函数的定义。

Theta state is what children are usually in as far as their brainwaves go.

θ脑波状态是孩子们的大脑波通常所处的状态。

But now the key is, how do we get to theta?

但现在关键在于，我们如何进入θ波状态？

Theta waves, which is the next brain we're talking about.

接下来我们要讨论的是Theta波，这是我们提到的下一个“脑”。

And theta is when you go into the dream state, very restful sleep.

而 Theta 状态就是当你进入梦境状态，一种非常放松的睡眠。

But let's go back to the alpha theta border.

但让我们回到阿尔法和 Theta 边界的讨论。

" d" theta, which I like to think of as signaling the fact that some kind of limit is being taken.

“d”theta，我喜欢将其视为表明 正在采取某种限制的事实。