Inverse Trigonometric Function

Inverse Trignometric Function Examples

Here you will learn some inverse trignometric function examples for better understanding of inverse trigonometric function concepts. Example 1 : Find the value of \(sin^{-1}({-\sqrt{3}\over 2})\) + \(cos^{-1}(cos({7\pi\over 6}))\). Solution : \(sin^{-1}({-\sqrt{3}\over 2})\) = – \(sin^{-1}({\sqrt{3}\over 2})\) = \(-\pi\over 3\) \(cos^{-1}(cos({7\pi\over 6}))\) = \(cos^{-1}(cos({2\pi – {5\pi\over 6}}))\) = \(cos^{-1}(cos({5\pi\over 6}))\) = \(5\pi\over 6\) Hence \(sin^{-1}({-\sqrt{3}\over …

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Formulas for Inverse Trigonometric Functions

Here, you will learn formulas for inverse trigonometric functions, equation and inequations involving inverse trigonometric function. Let’s begin – Simplified Inverse Trigonometric Functions (a)  y = f(x) = \(sin^{-1}({2x\over {1+x^2}})\) = \(\begin{cases} 2tan^{-1}x, & \text{if}\ |x| \le 1 \\ \pi – 2tan^{-1}x, & \text{if}\ x > 1 \\ -(\pi + 2tan^{-1}x), & \text{if}\ x < …

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Properties of Inverse Trigonometric Functions with Example

Here, you will learn all the properties of inverse trigonometric functions class 12 with examples. Let’s begin – Properties of Inverse Trigonometric functions Property – 1 (i)  y = \(sin^{-1}(sinx)\), x \(\in\) R, y \(\in\) (-\(\pi\over 2\), \(\pi\over 2\)) periodic with period \(2\pi\)and it is an odd function. (ii)  y = \(cos^{-1}(cosx)\), x \(\in\) R, …

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Inverse Trigonometric Function Class 12 – Domain & Range

Here, you will learn domain and range of inverse trigonometric function class 12. Let’s begin –  Inverse Trigonometric Function The inverse trigonometric functions, denoted by \(sin^{-1}x\) or (arc sinx), \(cos^{-1}x\) etc., denote the angles whose sine, cosine etc, is equal to x. The angles are usually smallest angles, except in case of \(cot^{-1}x\) and if …

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