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Inverse Trigonometric Functions

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Questions and Answers

What is the range of the inverse sine function?

(-π/2, π/2)

[-1, 1]

[0, π]

[-π/2, π/2] (correct)

What is the notation for the inverse cosine function?

arccos(x) (correct)

tan^-1(x)

arcsin(x)

sin(x)

What is the domain of the inverse tangent function?

[-1, 1]

[0, π]

(-π/2, π/2)

ℝ (all real numbers) (correct)

What is the characteristic of the graph of y = arcsin(x)?

It is symmetric about the origin Signup and view all the answers

What is the identity for arcsin(x) when x < 0?

arcsin(x) = -arccos(√(1 - x^2)) Signup and view all the answers

What is the trigonometric identity for sin(arcsin(x))?

sin(arcsin(x)) = x Signup and view all the answers

Study Notes

Inverse Trigonometry

arcsin (sin^-1)

Also known as the inverse sine function
Defined as the angle whose sine is a given value
Notation: arcsin(x) or sin^-1(x)
Domain: [-1, 1]
Range: [-π/2, π/2]

arccos (cos^-1)

Also known as the inverse cosine function
Defined as the angle whose cosine is a given value
Notation: arccos(x) or cos^-1(x)
Domain: [-1, 1]
Range: [0, π]

arctan (tan^-1)

Also known as the inverse tangent function
Defined as the angle whose tangent is a given value
Notation: arctan(x) or tan^-1(x)
Domain: ℝ (all real numbers)
Range: (-π/2, π/2)

Inverse Sine Graph

The graph of y = arcsin(x) is symmetric about the origin
The graph has a horizontal asymptote at y = π/2 and a horizontal asymptote at y = -π/2
The graph is increasing on its entire domain

Trigonometric Identities

sin(arcsin(x)) = x
cos(arccos(x)) = x
tan(arctan(x)) = x
arcsin(x) = arccos(√(1 - x^2)) for x ≥ 0
arcsin(x) = -arccos(√(1 - x^2)) for x < 0

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Description

Test your knowledge of inverse trigonometric functions, including arcsin, arccos, arctan, and their graphs, domains, and ranges. Learn about the properties and identities of these functions.