Explore a comprehensive 10-hour video series on inverse trigonometric functions. Delve into the fundamentals, including function relationships, derivatives, integrals, and graphing techniques. Master related rates problems, area calculations, and multiple inverse trig function evaluations. Learn to differentiate and integrate inverse trig functions, including chain rule applications. Analyze graphical properties, domain restrictions, and function transformations. Tackle exam-style problems and identity questions. Gain insights into the relationships between trigonometric and inverse trigonometric functions, their properties, and graphical representations. Perfect for students seeking a deep understanding of this essential calculus topic.
Overview
Syllabus
Introduction to Inverse Trig Functions (1 of 2): Why a whole new topic?.
Introduction to Inverse Trig Functions (2 of 2): Reviewing Functions & Relations.
Related Rates - Boat w/ Inverse Trig.
Derivatives of Inverse Trigonometric Functions.
Areas Involving Inverse Trig Functions.
Evaluating Multiple Inverse Trig Functions.
Inverse Trigonometric Functions: sin¯¹(x) & cos¯¹(x).
Inverse Trigonometric Functions: tan¯¹(x).
Graphing y = cos¯¹(cos x).
Graphing y = sin[sin¯¹(x)].
Graphing y = sin¯¹(sin x).
Graphing y = tan¯¹(tan x).
Evaluating Trig & Inv Trig Ratios (1 of 2).
Evaluating Trig & Inv Trig Ratios (2 of 2).
Differentiating sin¯¹(x) & cos¯¹(x).
Differentiating tan¯¹(x).
Inverse Trig + Trig Expansions: With Algebraic Terms.
Inverse Trig + Trig Expansions: With Values.
Inverse Trig Derivatives & Integrals (Summary).
Differentiating Inverse Trig Functions w/ Chain Rule (1 of 3).
Differentiating Inverse Trig Functions w/ Chain Rule (2 of 3).
Differentiating Inverse Trig Functions w/ Chain Rule (3 of 3).
Max/Min Question w/ Inverse Trig.
Indefinite Integrals of Inverse Trig Functions (1 of 2).
Indefinite Integrals of Inverse Trig Functions (2 of 2).
Graphing Inverse Trig Functions (1 of 2).
Graphing Inverse Trig Functions (2 of 2).
Tricky Inverse Trig Integral: The Easy Way.
Tricky Inverse Trig Integral: The Hard Way.
Inverse Trig Function w/ Complicated Argument.
Introduction to Inverse Functions (warning: out of focus).
Considering Inverse Trigonometric Expressions as Angles in Triangles.
Does sin¯¹(sin x) = x?.
Forming Inverse Functions by Restricting Domain.
Geometric Properties of Inverse Functions.
Graphing Functions & Their Inverses.
Restricting the Domain of cos x.
Tricky Inverse Trigonometric Expression Question.
Graphical & Analytical Approach to sin¯¹(sin x).
Differentiating sin inverse x by Considering Domain.
Functions, Domains and Fussy Eaters.
Further Thoughts on the Derivatives of Inverse Trigonometric Functions.
Interpreting sin¯¹(cos x).
Integrals Involving Inverse Trigonometric Functions & Reverse Chain Rule.
Standard Integrals Involving Inverse Trigonometric Functions.
How to Approach Areas Under Inverse Trig. Functions (1 of 2).
How to Approach Areas Under Inverse Trig. Functions (2 of 2).
Inverse Tan Identity Question (1 of 3): Complementary Identity.
Inverse Tan Identity Question (2 of 3): Addressing the Restrictions.
Inverse Tan Identity Question (3 of 3): Combining Terms & Graphing.
Modified Inverse Trig Graph: Determine Features & Evaluate Area.
Evaluating Trig Ratio of Inverse Trig Expression.
Exam Problem: Inverse Trig Identity.
Integration of Trigonometric Functions (1 of 3: Introduction to uses and some examples).
Integration of Trigonometric Functions (2 of 3: Manipulating the function to simplify integral).
Integration of Trigonometric Functions (3 of 3: Using Trig Identities to evaluate cos^2(x)).
Properties of Inverse Functions (1 of 3: If f(x) is increasing, f¯¹(x) is also increasing).
Inverse Trigonometric Functions (1 of 4: Choosing a Domain for the Inverse of sine).
Inverse Trigonometric Functions (2 of 4: Justifying the Choice of Domain).
Properties of Inverse Functions (2 of 3: Relationship of derivatives of the original and inverse).
Properties of Inverse Functions (3 of 3: Relationship between inverse and original symmetry).
Graphs of the Inverse Trig Functions (1 of 3: Reviewing the domain, range and shape).
Inverse Trigonometric Functions (3 of 4: Determining the domain of cos¯¹x and tan¯¹x).
Inverse Trigonometric Functions (4 of 4: Graphing the Shape of the inverse Trig Functions).
Graphs of the Inverse Trig Functions (2 of 3: Transformations of the basic inverse trig functions).
Graphs of the Inverse Trig Functions (3 of 3: WARNING - Shifting and transforming the WRONG way).
Properties of Graphs of I.T.Fs (1 of 3: Graphically and Algebraically Solving sin¯¹x + cos¯¹x = ?).
Properties of Graphs of I.T.Fs (2 of 3: Finding the solution to the compound function of arc(trig)x).
Properties of Graphs of I.T.Fs (3 of 3: Showing the Relationship between original & Compound).
Combining Trigonometric & Inverse Trigonometric Functions.
Graphs of Inverse Trigonometric Functions (1 of 2: Thinking through domain & range).
Graphs of Inverse Trigonometric Functions (2 of 2: Considering shifts through domain).
Taught by
Eddie Woo
