Class 12 Exam > Class 12 Questions > [-1, 1] is the domain for which of the follow...
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[-1, 1] is the domain for which of the following inverse trigonometric functions?
- a)sin-1x
- b)cot-1x
- c)tan-1x
- d)sec-1x
Correct answer is option 'A'. Can you explain this answer?
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[-1, 1] is the domain for which of the following inverse trigonometric...
Domain of Inverse Trigonometric Functions
The domain of an inverse trigonometric function is the range of the corresponding trigonometric function. In this case, the domain of the inverse trigonometric function is given as [-1, 1].
Explanation:
- sin-1x: The domain of sin-1x (also denoted as arcsin x) is [-1, 1]. This is because the range of sin(x) is [-1, 1], and when we take the inverse function, the roles of the input and output are reversed. Therefore, the domain of sin-1x is [-1, 1].
- cot-1x, tan-1x, sec-1x: The domains of these inverse trigonometric functions are different from sin-1x. For cot-1x, tan-1x, and sec-1x, the domains are not restricted to [-1, 1]. Therefore, they do not have the same domain as sin-1x.
Therefore, the correct answer is option 'A' sin-1x, as its domain matches the given domain of [-1, 1].
The domain of an inverse trigonometric function is the range of the corresponding trigonometric function. In this case, the domain of the inverse trigonometric function is given as [-1, 1].
Explanation:
- sin-1x: The domain of sin-1x (also denoted as arcsin x) is [-1, 1]. This is because the range of sin(x) is [-1, 1], and when we take the inverse function, the roles of the input and output are reversed. Therefore, the domain of sin-1x is [-1, 1].
- cot-1x, tan-1x, sec-1x: The domains of these inverse trigonometric functions are different from sin-1x. For cot-1x, tan-1x, and sec-1x, the domains are not restricted to [-1, 1]. Therefore, they do not have the same domain as sin-1x.
Therefore, the correct answer is option 'A' sin-1x, as its domain matches the given domain of [-1, 1].
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Community Answer
[-1, 1] is the domain for which of the following inverse trigonometric...
[-1, 1] is the domain for sin-1x.
The domain for cot-1x is (-∞,∞).
The domain for tan-1x is (-∞,∞).
The domain for sec-1x is (-∞,-1] ∪ [1,∞).
The domain for cot-1x is (-∞,∞).
The domain for tan-1x is (-∞,∞).
The domain for sec-1x is (-∞,-1] ∪ [1,∞).
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