alleryStart learning →Sort each inverse function into its domain
Exercise and reference answers
- Items
- Item
- sin⁻¹ x
- Category
- [−1, 1]
- Item
- cos⁻¹ x
- Category
- [−1, 1]
- Item
- cosec⁻¹ x
- Category
- R − (−1, 1)
- Item
- sec⁻¹ x
- Category
- R − (−1, 1)
- Item
- tan⁻¹ x
- Category
- R
- Item
- cot⁻¹ x
- Category
- R
- Categories
- Item
- [−1, 1]
- Item
- R − (−1, 1)
- Item
- R
Explanation
Only sin⁻¹ and cos⁻¹ accept every value from −1 to 1. cosec⁻¹ and sec⁻¹ need |x| ≥ 1, so the open middle is cut out.
tan⁻¹ and cot⁻¹ accept any real number.
Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.
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