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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?
- All real numbers
- $[- rac{ u}{2}, rac{ u}{2}]$ (correct)
- $[- rac{ u}{2}, u]$
- $[- rac{ u}{2}, 1]$
Which equation correctly represents the result of finding the arcsine of 1?
Which equation correctly represents the result of finding the arcsine of 1?
- $1$
- $ rac{ u}{2}$ (correct)
- $ u$
- $0$
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?
- $0$
- $2$ (correct)
- $1$
- $3$
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$?
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?
Flashcards
Inverse Sine Function
Inverse Sine Function
The inverse sine function, often written as sin⁻¹(x) or arcsin(x), finds the angle (in radians) whose sine is x.
Domain of arcsin(x)
Domain of arcsin(x)
The set of input values (x) for which the inverse sine function is defined. It is typically -1 ≤ x ≤ 1.
Range of arcsin(x)
Range of arcsin(x)
The set of output values (angles in radians) produced by the inverse sine function. It is typically -π/2 ≤ y ≤ π/2.
arcsin(1)
arcsin(1)
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arcsin(-1)
arcsin(-1)
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sin(π/2)
sin(π/2)
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sin(nπ)
sin(nπ)
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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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