Overview
This section covers the following concepts: Derivatives of tan(x), cot(x), sec(x), and csc(x).
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
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(Review) Apply all the derivative rules from Sections 2.1, 2.2 and 2.3 with fluency.
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(Review) Review the basic properties of all six main trigonometric functions: definition, domain, graph, values of the function at the main angles (\(0,\pi/6,\pi/4,\pi/3,\pi/2\) and all geometrically related angles), related trigonometric identities. (See section 0.5 of Caroll University’s additional chapter 0 for Active Calculus, and this handout on properties of trigonometric functions.)
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State the derivatives of \(y=\tan x\), \(y=\sec x\), \(y=\cot x\), and \(y=\csc x\).
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
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Derive the derivatives of \(y=\tan x\), \(y=\sec x\), \(y=\cot x\), and \(y=\csc x\) “from scratch” using only basic derivative rules and trigonometric identities.
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Differentiate a function for which the derivative involves a combination of these trigonometric functions, and other rules we’ve learned.
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Use all rules learned so far in the context of a real-world problem to find the slope of a tangent line, the instantaneous rate of change in a function, or the instantaneous velocity of an object.
To prepare for class
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Watch the following video to help you review some basic facts about the 6 trigonometric functions and their relationships (video created at CCSL):
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(As necessary), read and review section 0.5 of Caroll University’s additional chapter 0 for Active Calculus, as well as this handout on properties of trigonometric functions.
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Do the Preview Activity for this section (on WeBWorK if required by your teacher).
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Read subsection 2.4.1, which goes through the calculation of finding the derivative of \(\cot(x)\).
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Watch the following videos:
