Derivatives of Trigonometric Functions
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Lesson Summary:
In this lesson, we learned about the derivatives of trigonometric functions, including sine, cosine, tangent, cotangent, secant, and cosecant. We discovered that the derivative of each function has a specific pattern, and by remembering this pattern, we only need to remember three derivatives. We also saw examples of how to apply the product and quotient rules to find derivatives of more complex functions involving trigonometric functions.
Lesson Description:
The derivatives of sin, cos, tan, cot, sec, csc.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Additional Resources:
- Differentiating the Trigonometric Functions - Practice Differentiating the Trigonometric Functions.
- Table of Derivatives - Table of derivatives of several different functions.
- Derivatives and Integrals of Trig Functions - A list of derivatives and integrals of various trig functions.
Questions answered by this video:
- What is the derivative of sin x?
- What is the derivative of cos x?
- Why does the derivative of sin x = cos x?
- Why does the derivative of cos x = - sin x?
- What is the derivative of tan x?
- What is the derivative of cot x?
- What is the derivative of sec x?
- What is the derivative of csc x?
- What is the derivative of sec x tan x?
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Staff Review
This video begins with some great animations showing the graphs of the derivatives of sin x and cos x. Then, we find the derivative using the formal definition of a derivative. This assumes that you have some trig foundation. The steps are done quickly, but are shown completely. Then, some examples of trig derivatives are shown. Finally, the derivatives of the other trig functions are found.
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