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Inverse Trigonometric Functions Class 12 Notes Maths Chapter 2

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FAQs on Inverse Trigonometric Functions Class 12 Notes Maths Chapter 2

1. What are inverse trigonometric functions?
Ans. Inverse trigonometric functions are mathematical functions that provide the angle value for a given trigonometric ratio. They reverse the process of trigonometric functions, allowing us to find the angle when the ratio is known.
2. How are inverse trigonometric functions denoted?
Ans. Inverse trigonometric functions are denoted by the prefix "arc" or "a" before the trigonometric function abbreviation. For example, the inverse of sine is denoted as "arcsin" or "asin," the inverse of cosine is "arccos" or "acos," and the inverse of tangent is "arctan" or "atan."
3. What is the domain and range of inverse trigonometric functions?
Ans. The domain of inverse trigonometric functions depends on the range of the corresponding trigonometric function. For arcsin and arccos, the domain is [-1, 1], and the range is [-π/2, π/2]. For arctan, the domain is (-∞, ∞), and the range is (-π/2, π/2).
4. How are inverse trigonometric functions used in solving equations?
Ans. Inverse trigonometric functions are used to solve equations involving trigonometric ratios. By applying the appropriate inverse function, we can find the angle values that satisfy the equation. These functions are particularly useful in solving trigonometric equations and determining unknown angles.
5. What are the identities and properties of inverse trigonometric functions?
Ans. The identities and properties of inverse trigonometric functions include: - The principal value: Inverse trigonometric functions have a principal value within a specific range, usually denoted as the principal branch. This ensures uniqueness and consistency in the output. - Symmetry: The inverse trigonometric functions exhibit symmetry around the origin, meaning that the inverse of a positive value yields a positive angle, and the inverse of a negative value yields a negative angle. - Complementarity: The inverse trigonometric functions have complementary relationships, such as arcsin(x) + arccos(x) = π/2 and arctan(x) + arccot(x) = π/2. - Inverse of composite functions: The inverse trigonometric functions can be used to find the inverse of composite functions involving trigonometric ratios. These identities and properties help in understanding and utilizing inverse trigonometric functions effectively.
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