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NCERT Solutions Class 12 Maths Chapter 2 - Inverse Trigonometric Functions

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FAQs on NCERT Solutions Class 12 Maths Chapter 2 - Inverse Trigonometric Functions

1. What are inverse trigonometric functions?
Ans. Inverse trigonometric functions are mathematical functions that help us find the angle or angles corresponding to a given trigonometric ratio. For example, if we know the sine of an angle, the inverse sine function can help us find the angle itself.
2. How are inverse trigonometric functions denoted?
Ans. Inverse trigonometric functions are denoted by adding a "-1" superscript to the trigonometric function. For example, inverse sine is denoted as sin^-1, inverse cosine as cos^-1, and so on.
3. What is the domain and range of inverse trigonometric functions?
Ans. The domain of inverse trigonometric functions depends on the specific function. Generally, the domain of inverse sine and inverse cosine functions is [-1, 1], while the domain of inverse tangent function is (-∞, ∞). The range of all inverse trigonometric functions is typically given by the interval [-π/2, π/2] or (-π/2, π/2).
4. How are inverse trigonometric functions used in real-world applications?
Ans. Inverse trigonometric functions find applications in various fields such as physics, engineering, and navigation. They are used to solve problems involving angles, distances, heights, and trajectories. For example, inverse trigonometric functions can help calculate the angle of elevation or depression in surveying or determine the position of a moving object.
5. Do inverse trigonometric functions have unique solutions?
Ans. Inverse trigonometric functions may have multiple solutions depending on the given trigonometric ratio. For example, inverse sine has infinitely many solutions because sine is a periodic function. To obtain a unique solution, additional conditions or restrictions may need to be imposed, such as specifying the range of the inverse function.
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