Final answer:
The domains and ranges of the inverse trigonometric functions ¹sin(x), ¹cos(x), and ¹tan(x) are as follows: ¹sin(x) has a domain of [-1, 1] and range of [-π/2, π/2], ¹cos(x) has a domain of [-1, 1] and range of [0, π], and ¹tan(x) has a domain of all real numbers and a range of (-π/2, π/2).
Step-by-step explanation:
The question asks for the domain and range of the inverse trigonometric functions ¹sin(x), ¹cos(x), and ¹tan(x). Here is the domain and range of each function:
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- The domain of ¹sin(x) is [-1, 1] and its range is [-π/2, π/2].
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- The domain of ¹cos(x) is [-1, 1] and its range is [0,π].
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- The domain of ¹tan(x) is all real numbers and its range is (-π/2, π/2).
Understanding these domains and ranges is essential for correctly applying these functions in various mathematical contexts.