Master How to determine the domain and range of the inverse trigonometric functions

The video tutorial covers the domain and range of sine, cosine, and tangent functions, and their inverses. It explains how to identify these properties using graphs and discusses the importance of restricting the range for inverse functions to ensure they remain functions. The tutorial also demonstrates how to graph inverse trigonometric functions by swapping coordinates and reflecting them about the y=x line.

What is the domain of the sine function?

• From -1 to 1

• From 0 to π

• From -π/2 to π/2

• From negative infinity to infinity

What is the range of the cosine function?

• From -1 to 1

• From 0 to π

• From -π/2 to π/2

• From negative infinity to infinity

Which of the following describes the domain of the tangent function?

• From 0 to π

• From -1 to 1

• All real numbers except where asymptotes occur

• All real numbers

How do you find the inverse of a function graphically?

• By translating the graph upwards

• By reflecting the graph about the line y = x

• By reflecting the graph about the y-axis

• By rotating the graph 90 degrees

What happens to the domain and range when finding the inverse of a trigonometric function?

• They are swapped

• They are doubled

• They remain the same

• They are halved

Why do we restrict the range of inverse sine and cosine functions?

• To make them periodic

• To ensure they remain functions

• To decrease their domain

• To increase their domain

What is the restricted range for the inverse sine function?

• From -1 to 1

• From -π/2 to π/2

• From 0 to π

• From negative infinity to infinity

What is the restricted range for the inverse cosine function?

• From -1 to 1

• From negative infinity to infinity

• From 0 to π

• From -π/2 to π/2

What is the range of the inverse tangent function?

• From -π/2 to π/2

• From negative infinity to infinity

• From 0 to π

• From -1 to 1

Why is it important to restrict the range of inverse trigonometric functions?

• To increase their domain

• To make them periodic

• To make them continuous

• To ensure they are one-to-one