Session 8: Limits of Sine and Cosine

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Overview

When we tried to differentiate the sine and cosine functions we were left with two limits to calculate. In this session Professor Jerison calculates these limits, taking a close look at the unit circle and applying some fundamental ideas from linear approximation.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Limit of sin(x)/x (5 min)
» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Limit of (1-cos(x))/x (4 min)
» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Questions and Answers (11 min)
» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

» Clip 4: Derivative of sin(x), Geometric Proof (12 min)
» Accompanying Notes (PDF)

From Lecture 3 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

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Worked Example

The Function sinc(x)

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Session 8: Limits of Sine and Cosine

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Worked Example

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