Domain and range of inverse trigonometric functions.
Understand the Problem
The question provides a table summarizing the domains and ranges of inverse trigonometric functions. It includes functions like sin-1, cos-1, tan-1, cot-1, and sec-1. The user is likely looking for more information on these functions, either for study or application in a problem.
Answer
Inverse trigonometric domains and ranges: 1. sin⁻¹(x): Domain [-1, 1], Range [-π/2, π/2]. 2. cos⁻¹(x): Domain [-1, 1], Range [0, π]. 3. tan⁻¹(x): Domain (-∞, ∞), Range (-π/2, π/2). 4. cot⁻¹(x): Domain (-∞, ∞), Range (0, π). 5. sec⁻¹(x): Domain (-∞, -1] ∪ [1, ∞), Range [0, π/2) ∪ (π/2, π].
The inverse trigonometric functions have the following domains and ranges:
- sin⁻¹(x): Domain is [-1, 1], Range is [-π/2, π/2].
- cos⁻¹(x): Domain is [-1, 1], Range is [0, π].
- tan⁻¹(x): Domain is (-∞, ∞), Range is (-π/2, π/2).
- cot⁻¹(x): Domain is (-∞, ∞), Range is (0, π).
- sec⁻¹(x): Domain is (-∞, -1] ∪ [1, ∞), Range is [0, π/2) ∪ (π/2, π].
Answer for screen readers
The inverse trigonometric functions have the following domains and ranges:
- sin⁻¹(x): Domain is [-1, 1], Range is [-π/2, π/2].
- cos⁻¹(x): Domain is [-1, 1], Range is [0, π].
- tan⁻¹(x): Domain is (-∞, ∞), Range is (-π/2, π/2).
- cot⁻¹(x): Domain is (-∞, ∞), Range is (0, π).
- sec⁻¹(x): Domain is (-∞, -1] ∪ [1, ∞), Range is [0, π/2) ∪ (π/2, π].
More Information
The inverse trigonometric functions reverse the operation of the standard trigonometric functions, converting a ratio back into an angle.
Tips
A common mistake is confusing the domain and range of trigonometric functions with those of their inverses.
Sources
- Inverse Trigonometric Functions - Varsity Tutors - varsitytutors.com
- Inverse Trigonometric Functions | Precalculus - courses.lumenlearning.com
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