Class 12 Mathematics — Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS

What you'll learn

• ▸Conditions for Inverse Functions
• ▸Inverse Sine Function (sin⁻¹x)
• ▸Inverse Cosine Function (cos⁻¹x)
• ▸Inverse Tangent Function (tan⁻¹x)
• ▸Inverse Cosecant & Secant Functions (cosec⁻¹x, sec⁻¹x)
• ▸Summary of Domains and Principal Value Ranges
• ▸Graphical Representation of Inverse Trigonometric Functions

Chapter Summary

--- PAGE 1 --- --- PAGE 2 --- INVERSE TRIGONOMETRIC FUNCTIONS 19 We have also learnt in Chapter 1 that if f: X→Y such that f(x) = y is one-one and onto, then we can define a unique function g : Y→X such that g(y) = x, where x ∈ X and y ∈ Y(x), y ∈ Y. Here, the domain of g = range of f and the range of g = domain of f. The function g is called the inverse of f and is denoted by f⁻¹. Further, g is also one-one and onto and inverse of g is f. Thus, g⁻¹ = (f⁻¹)⁻¹ = f. We also have (f⁻¹ o f) (x) = f⁻¹ (f (x)) = f⁻¹(y) = x and (f o f⁻¹) (y) = f (f⁻¹(y)) = f(x) = y Since the domain of sine function is the set of all real numbers and range is the closed interval [–1, 1]. If we restrict its domain to [-π/2, π/2], then it becomes one-one and onto with range [–1, 1]. Actually, sine function restricted to any of the intervals [-3π/2, -π/2], [-π/2, π/2], [π/2, 3π/2] etc., is one-one and its range is [–1, 1]. We can, therefore, define the inverse of sine funct…

Practice Questions from this Chapter

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1. Visualize inverse function graphs easily? Get Solution →
2. Apply inverse trig to real life? Get Solution →
3. Explore angles beyond a circle? Get Solution →
4. What is the domain of the inverse sine function, sin⁻¹(x)? Get Solution →
5. What is the range of the principal value branch of the inverse cosine function, cos⁻¹(x)? Get Solution →
6. Which of the following represents the principal value branch range for the inverse tangent function, tan⁻¹(x)? Get Solution →
7. What does the notation (sin x)⁻¹ represent? Get Solution →
8. The value of an inverse trigonometric function that lies in the range of the principal branch is called the: Get Solution →

Did you know?

• 💡 Encryption and decryption are perfect real-world examples of functions and their inverses.
• 💡 Ancient civilizations used early forms of trigonometry for astronomy and navigation.
• 💡 The number Pi, central to circles, never repeats and goes on infinitely.
• 💡 Sound waves and light waves can be described using trigonometric functions.
• 💡 A mathematical function is like a machine that takes an input and gives exactly one output.

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