Inverse Trigonometric Functions - Evaluating the Composition of Inverse Trigonometric Functions

Explore inverse trigonometric functions and their compositions in this comprehensive 36-minute video lesson. Begin by revisiting one-to-one functions and the squaring function, then learn how to restrict domains and find inverses of trigonometric functions. Examine graphs of sine, cosine, and tangent functions along with their inverse counterparts. Practice solving problems involving inverse sine, cosine, tangent, cotangent, secant, and cosecant values. Conclude with a summary table of inverse trigonometric functions and work through examples to find exact values using these concepts.

Revisiting one-to-one functions.
Revisiting the squaring function f(x) = x^2.
Restricting the domain of the squaring function f(x) = x^2, x ≥ 0.
Finding the inverse of the domain restricted function f(x) = x^2, x ≥ 0.
Showing the graphs of f(x) = x^2, x ≥ 0, f(x) = sqrt(x), and y = x.
Showing the graph of y = sin x.
Showing the graph of y = sin x, -π/2 ≤ x ≤ π/2.
Showing the graph of y = arcsin x.
Finding inverse sine values problem #1.
Finding inverse sine values problem #2.
Showing the graph of y = cos x.
Showing the graph of y = cos x, 0 ≤ x ≤ π.
Showing the graph of y = arccos x.
Finding inverse cosine values problem #1.
Finding inverse cosine values problem #2.
Showing the graph of y = tan x.
Showing the graph of y = tan x, -π/2 < x < π/2.
Showing the graph of y = arctan x.
Finding inverse tangent values problem #1.
Inverse cotangent function.
Inverse secant function.
Inverse cosecant function.
Finding inverse cosecant values problem #1.
Summary table for inverse trigonometric functions.
Finding the exact value problem #1.
Finding the exact value problem #2.
Finding the exact value problem #3.