Inverse Trigonometric Functions
CBSE · Class 12 · Mathematics
Flashcards for Inverse Trigonometric Functions — CBSE Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allWhy don't inverse trigonometric functions exist for the original domains of trigonometric functions?
Answer
Trigonometric functions are not one-one (injective) over their natural domains. For a function to have an inverse, it must be both one-one and onto (bijective). Since sin x, cos x, etc. repeat their v…
What is the domain and range of sin⁻¹x?
Answer
Domain: [-1, 1] Range: [-π/2, π/2] This range is called the principal value branch of sin⁻¹x. The function sin⁻¹: [-1, 1] → [-π/2, π/2]…
What is the domain and range of cos⁻¹x?
Answer
Domain: [-1, 1] Range: [0, π] This range is the principal value branch of cos⁻¹x. The function cos⁻¹: [-1, 1] → [0, π]…
What is the domain and range of tan⁻¹x?
Answer
Domain: R (all real numbers) Range: (-π/2, π/2) This range is the principal value branch of tan⁻¹x. The function tan⁻¹: R → (-π/2, π/2)…
What is the domain and range of cot⁻¹x?
Answer
Domain: R (all real numbers) Range: (0, π) This range is the principal value branch of cot⁻¹x. The function cot⁻¹: R → (0, π)…
What is the domain and range of sec⁻¹x?
Answer
Domain: R - (-1, 1) or (-∞, -1] ∪ [1, ∞) Range: [0, π] - {π/2} This range is the principal value branch of sec⁻¹x. The function sec⁻¹: R - (-1, 1) → [0, π] - {π/2}…
What is the domain and range of cosec⁻¹x?
Answer
Domain: R - (-1, 1) or (-∞, -1] ∪ [1, ∞) Range: [-π/2, π/2] - {0} This range is the principal value branch of cosec⁻¹x. The function cosec⁻¹: R - (-1, 1) → [-π/2, π/2] - {0}…
What is meant by the principal value of an inverse trigonometric function?
Answer
The principal value of an inverse trigonometric function is the value that lies in the range of the principal value branch of that function. When we write sin⁻¹x, cos⁻¹x, etc., without specifying a br…
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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