Inverse Trigonometric Functions

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