Inverse Trigonometric Functions - II
Carefully understand the domain and range of following functions
4.
= R

You can observe from the above graph
, where x belongs to domain of arccot x
Comparison between the graph of arctan x and arccot x
You can observe from above graph,
, x belongs to R i.e. domain of arctan(x) and arccot(x)
5.
![Domain = ( - \infty , - 1]\bigcup {[1,\infty ) = R - ( - 1,1)}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tp5ba_BZX8tLSYmcZKt9bSZ2s4BXBZ1WCOgBR2nIT19kF-hwmsUuobDAwK6urDU5awEoqSv-IPKTJ76GZ6nkXqwxuOW4-Jn1codCjyR1nbhpXw1v4oCcRFqi5u5VeEFj8t0N0H8JU3RvDxOntJjIByV362sfXSe6vLMDMKbW-WCeSxoQRuw4-Zn2PKnDi4XXdnrtY_a2ua5OpyZAzFX-pkrapG-JmZcb9UWlG3F8QHjb2JWNrJYDlF9GXXDItUAHo60XEwu-7rmOU=s0-d)
![Range = \left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right] - \{ 0\}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tOnwRHSIx1sdf1yau6_-fLhFa2Mb6aMh6m5bXBblYlw5vfXkQsyon6uZMgKt2pNGOtK1iKwf5ZNzqaFQuhfRPRlRxbqikPM-EjG6QgDFf67oo7vWmsVRnjKsZhaEjNbgSgSsBb3yvmxt816MDLi6zVY42vOthlZdXFujR2_hA8RfMs1Ti7jheblofCXP_mfHsrijWiTVEAlk5FcirJWv_tH2caEqyxP7_skcSbczRGrRT4eQ8h4axAUKrtEvubC3e95owO69Kyf6n0GGa6eUAvExebYYAk4nQ2VI76HN0U70lPxaDJXxxBQA=s0-d)
You can observe,
, where x belongs to domain of arccosec(x)
6.
![Domain = ( - \infty , - 1]\bigcup {[1,\infty ) = R - ( - 1,1)}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tp5ba_BZX8tLSYmcZKt9bSZ2s4BXBZ1WCOgBR2nIT19kF-hwmsUuobDAwK6urDU5awEoqSv-IPKTJ76GZ6nkXqwxuOW4-Jn1codCjyR1nbhpXw1v4oCcRFqi5u5VeEFj8t0N0H8JU3RvDxOntJjIByV362sfXSe6vLMDMKbW-WCeSxoQRuw4-Zn2PKnDi4XXdnrtY_a2ua5OpyZAzFX-pkrapG-JmZcb9UWlG3F8QHjb2JWNrJYDlF9GXXDItUAHo60XEwu-7rmOU=s0-d)
![Range = [0,\pi ] - \left\{ {\frac{\pi }{2}} \right\}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sBK3QwDHI1t-2WySvEKw0zjO8GiocnIThes5fiwvL_1oU82GaN1yyrMiejdQWqY2V49CxNOH_zbkDjTloN-wuUAAhDPVUEh9SthH2boNOlpmqhjFLZc8xZrkfzuAhhWTUjXcrdYAp2OGtUwM41NAPBAbQjuvIgGwp4bYryiRWtov759SKtn7sX9Un1kudoJs3a0Nei97QOOXTJjgw4XGC5oenlS_FRGfj6CiDkH-lIO73D-0eGkkdbTlf-Gbz821LdJEamGaGa93VEBBO9NKQI=s0-d)
From the above graph, you can observe
, x belongs to domain of arcsec(x)
Comparison between the graph of arccosec x and arcsec x
Observation from above graph,
, where x belongs to domain of arccosec(x) or arcsec(x)
4.
You can observe from the above graph
Comparison between the graph of arctan x and arccot x
You can observe from above graph,
5.
You can observe,
6.
From the above graph, you can observe
Comparison between the graph of arccosec x and arcsec x
Observation from above graph,





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