Maths > Inverse Trigonometric Function > 2.0 Inverse Trigonometric function
Inverse Trigonometric Function
1.0 Introduction
2.0 Inverse Trigonometric function
2.1 ${\sin ^{ - 1}}x$:
2.2 ${\cos ^{ - 1}}x$:
2.3 ${\tan ^{ - 1}}x$:
2.4 ${\text{cose}}{{\text{c}}^{ - 1}}x$:
2.5 ${\sec^{ - 1}}x$
2.6 ${\cot^{ - 1}}x$
2.7 Summary
3.0 Properties
3.1 Property 1
3.2 Property 2
3.3 Property 3
3.4 Property 4
3.5 Property 5
3.6 Property 6
3.7 Property 7
3.8 Property 8
3.9 Property 9
3.10 Property 10
3.11 Property 11
3.12 Property 12
3.13 Property 13
2.7 Summary
2.2 ${\cos ^{ - 1}}x$:
2.3 ${\tan ^{ - 1}}x$:
2.4 ${\text{cose}}{{\text{c}}^{ - 1}}x$:
2.5 ${\sec^{ - 1}}x$
2.6 ${\cot^{ - 1}}x$
2.7 Summary
3.2 Property 2
3.3 Property 3
3.4 Property 4
3.5 Property 5
3.6 Property 6
3.7 Property 7
3.8 Property 8
3.9 Property 9
3.10 Property 10
3.11 Property 11
3.12 Property 12
3.13 Property 13
We can summarize the domain and range of inverse trigonometric functions as follows
| Inverse trigononmetric functions | Domain | Range |
| ${\sin ^{ - 1}}x$ | $[-1,1]$ | $\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]$ |
| ${\cos ^{ - 1}}x$ | $[-1,1]$ | $[0,\pi ]$ |
| ${\tan ^{ - 1}}x$ | $R$ | $R - \{ (2n + 1)\frac{\pi }{2}\} $ |
| ${\text{cose}}{{\text{c}}^{ - 1}}x$ | $R - ( - 1,1)$ | $\left[ {-\frac{\pi }{2}, \frac{\pi }{2}} \right] - \left\{ 0 \right\}$ |
| ${\sec ^{ - 1}}x$ | $R - ( - 1,1)$ | $\left[ {0,\pi } \right] - \left\{ {\frac{\pi }{2}} \right\}$ |
| ${\cot ^{ - 1}}x$ | $R$ | $\left( {0,\pi } \right)$ |
Note:
- The graph of inverse trigonometric functions is drawn by taking the mirror image of portion of original function within the principal value set of domain and range.
- If domain and range are not mentioned in the question, then we need to consider the principal values.
