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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?
Which equation correctly represents the result of finding the arcsine of 1?
Which equation correctly represents the result of finding the arcsine of 1?
What is the input value for which the inverse sine function is not defined?
What is the input value for which the inverse sine function is not defined?
Which of the following points is correctly indicating where $ ext{sin}(x) = 1$?
Which of the following points is correctly indicating where $ ext{sin}(x) = 1$?
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Which statement accurately describes the relationship between the sine function and its inverse sine function?
Which statement accurately describes the relationship between the sine function and its inverse sine function?
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Study Notes
Inverse Trigonometric Function
- Inverse Sine Function: The inverse sine function, denoted as sin⁻¹(x) or arcsin(x), is the inverse of the sine function.
- Domain: The domain of the inverse sine function is [-1, 1]. Values outside this range are undefined.
- Range: The range of the inverse sine function is [-π/2, π/2].
- Sin(π/2) = 1: sin⁻¹(1) = π/2
- Sin(-π/2) = -1: sin⁻¹(-1) = -π/2
- Sin(3) = Undefined: The input 3 is not within the domain of the arcsin function [-1, 1].
Key Properties of Sine and Sine Inverse
- Domain of sin(x): All real numbers.
- Range of sin(x):[-1, 1]
- Domain of sin⁻¹(x):[-1, 1]
- Range of sin⁻¹(x):[-π/2, π/2]
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Description
Explore the properties and characteristics of inverse sine functions. This quiz covers the domain, range, and key equations related to arcsin(x). Test your understanding of how these functions interact with the sine function.
