标签：phi sinx very 一个角 small theta sin

以下内容转载自https://math.stackexchange.com/questions/870092/why-is-sind-phi-d-phi-where-d-phi-is-very-small

其中一个答案是：

Just draw the diagram!

What does sinx mean? it's the ratio of the opposite side to the hypotenuse in a triangle.

Now, let's draw a triangle with a small angle x inside the unit circle:

Now clearly, when the angle becomes really small, the opposite side is approximately the arc length. In radians, the arc length in a unit circle is exactly the angle x, and so we have for small angles:

If you are familiar with Taylor series you know that the series of sin(x) expanded at 0 is:

Then, if x is very small you can neglect all term of order greater than one getting:

You can also show this result using basic trigonometry but this approach seems easier to me.

还有一个答案是：

You can give a linear approximation for sin near 0 based on this formula:

and using the fact that: sin′=cos, you get:

So when x is very small, you have that sinx∼x.

What this intuitively means, is that when you observe closely the graph of the curve sinx near 0, it starts to resemble a line, and this line is described by y=x.

XXX

标签：phi,sinx,very,一个角,small,theta,sin
来源： https://www.cnblogs.com/heweiren-cheng/p/15159285.html

本站声明： 1. iCode9 技术分享网（下文简称本站）提供的所有内容，仅供技术学习、探讨和分享；
2. 关于本站的所有留言、评论、转载及引用，纯属内容发起人的个人观点，与本站观点和立场无关；
3. 关于本站的所有言论和文字，纯属内容发起人的个人观点，与本站观点和立场无关；
4. 本站文章均是网友提供，不完全保证技术分享内容的完整性、准确性、时效性、风险性和版权归属；如您发现该文章侵犯了您的权益，可联系我们第一时间进行删除；
5. 本站为非盈利性的个人网站，所有内容不会用来进行牟利，也不会利用任何形式的广告来间接获益，纯粹是为了广大技术爱好者提供技术内容和技术思想的分享性交流网站。