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Properties of Inverse Trigonometric Functions Video Lecture | Mathematics (Maths) for JEE Main & Advanced
FAQs on Properties of Inverse Trigonometric Functions Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What are the domains and ranges of inverse trigonometric functions? |  |
Ans. The domains and ranges of inverse trigonometric functions are as follows:
- $\arcsin(x)$: Domain $[-1, 1]$, Range $[-\frac{\pi}{2}, \frac{\pi}{2}]$
- $\arccos(x)$: Domain $[-1, 1]$, Range $[0, \pi]$
- $\arctan(x)$: Domain $(-\infty, \infty)$, Range $(-\frac{\pi}{2}, \frac{\pi}{2})$
| 2. How do you find the values of inverse trigonometric functions using a calculator? | |
Ans. To find the values of inverse trigonometric functions using a calculator, typically you would use the $\sin^{-1}$, $\cos^{-1}$, or $\tan^{-1}$ buttons on the calculator. Simply input the value you want to find the inverse of, then press the corresponding button to get the result.
| 3. How do you simplify expressions involving inverse trigonometric functions? | |
Ans. To simplify expressions involving inverse trigonometric functions, you can use trigonometric identities and properties. For example, you can use the fact that $\sin(\arcsin(x)) = x$ and $\arcsin(\sin(x)) = x$ to simplify expressions.
| 4. What are the important properties of inverse trigonometric functions? | |
Ans. Some important properties of inverse trigonometric functions include:
- $\sin(\arcsin(x)) = x$ and $\arcsin(\sin(x)) = x$
- $\cos(\arccos(x)) = x$ and $\arccos(\cos(x)) = x$
- $\tan(\arctan(x)) = x$ and $\arctan(\tan(x)) = x$
| 5. How do you prove identities involving inverse trigonometric functions? | |
Ans. To prove identities involving inverse trigonometric functions, you can use the definitions of the inverse trigonometric functions and trigonometric identities. By manipulating the expressions using these definitions and identities, you can prove the desired identity involving inverse trigonometric functions.
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