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Questions and Answers
What is the range of the inverse sine function?
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?
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?
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)?
What is the characteristic of the graph of y = arcsin(x)?
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What is the identity for arcsin(x) when x < 0?
What is the identity for arcsin(x) when x < 0?
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What is the trigonometric identity for sin(arcsin(x))?
What is the trigonometric identity for sin(arcsin(x))?
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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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