3.2 Derivatives of Trigonometric Functions

In this lesson, you will learn about trigonometric limits, derivatives or higher order derivatives of trigonometric functions, and other trigonometric functions using the derivative of the sine and/or cosine function.

Lesson Objectives

Upon completion of the lesson 3.2, you will be able to:

- Apply one or both special trigonometric limits as needed and/or when evaluating a trigonometric limit.
- Find the derivatives or higher order derivatives of trigonometric functions.
- Derive the derivative of other trigonometric functions using the derivative of the sine and/or cosine function and the basic differentiation rules.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

1. YouTube video: Two Special Trigonometric Limits

1. YouTube video: Proof that

1. YouTube video: Another Special Trigonometric Limit

1. YouTube video: Special Trigonometric Limits Examples

1. YouTube video: The derivative of the sine function

1. YouTube video: Derivative of Trigonometric Functions (cos & tan)

1. YouTube video: The derivatives of other trig functions (sec, csc, tan, cot)

1. YouTube video: Trigonometric derivatives examples
2. Example 1:

1. Example 2: (Start the video from 12:55)

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

Derivatives of Trigonometric Functions [Paul's Online Math Notes]

Read only to the end of example 2.

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

Additional Resources

Below are additional resources that help reinforce the content for this module.

1. Trigonometric Limits [University of Houston] (the limit of sin(x)/x as
2. and related limits) View pp. 6 - 9 only.
3. Derivatives of Trigonometric Functions [University of Houston] (the derivatives of sin x, cos x, tan x, cot x, sec x, csc x)
4. Derivatives of Trigonometric Functions [Wikibooks]

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