Derivative of sin x and cos x
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Video Lecture 7 of 18
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Date Added: June 4, 2011

### Lecture Description

The two key functions of oscillation have specially neat derivatives:
- The slope of sin x is cos x
- The slope of cos x is - sin x

These come from one crucial fact: (sin x) / x approaches 1 at x = 0. This checks that the slope of sin x is cos 0 = 1 at the all-important point x = 0. In this video lecture, Prof. Gilbert Strang connects sine and cosine to moving around a circle, or up and down for a spring, or in and out for your lungs.

### Course Description

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.

The series is divided into three sections:
Introduction
- Why Professor Strang created these videos
- How to use the materials

Highlights of Calculus
- Five videos reviewing the key topics and ideas of calculus
- Applications to real-life situations and problems
- Additional summary slides and practice problems

Derivatives
- Twelve videos focused on differential calculus
- More applications to real-life situations and problems
- Additional summary slides and practice problems

Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.