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_sl2JrTVewg_YvxYWzW1LUXg63w8Zm1lv6GHVgvP1b_v8d6gdpZLpCA59V2ZSs8PJLrnD2LZGFQHyZqnJ4vU_2SkazYce5gf-0YIeoTNlkUPsTEmjQzMECFTCHG0mKVM-9BNglAQJWgAp8vnKxZeewQM0jYcmtT8cQ-f1kYTT6Luh11o4LOLFki6uTlVR_xYc37DdB8DbN2vEFoGe88P0P3hydQ3AkdVjDd2GFIY3hkNY_7WKJ1cWua04v-w7spz3NuzsmGsXo-1vw=s0-d)
![Range = \left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right] - \{ 0\}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uh7Ai07R1U-pv7ElXICEILOJFkriFrzusUCxr49YGYkfXNyEr3a-g9g27d6hQO616mIe_j3qzuZwrYXD9mfXaFV9up9e0px3ognZOB--ViiFEIJVmws8Csn0xuyFFgFmwlcPcl8pdRHPJLYMC0l88yBeAKdbz1vsvr6oklT89lwnivyyEGwrwSlCzipOWQIqitq0t5YAay29gvwCG2wjbo38u57ilmOVr0pPcW9PG4NoeZ0n2jl98m8bOBJR5NClIUuXe1ZDuG2xmW8OOjoVB65JpNHP9bWg_KBL232iTvRuG8piM8ZuTyTQ=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_sl2JrTVewg_YvxYWzW1LUXg63w8Zm1lv6GHVgvP1b_v8d6gdpZLpCA59V2ZSs8PJLrnD2LZGFQHyZqnJ4vU_2SkazYce5gf-0YIeoTNlkUPsTEmjQzMECFTCHG0mKVM-9BNglAQJWgAp8vnKxZeewQM0jYcmtT8cQ-f1kYTT6Luh11o4LOLFki6uTlVR_xYc37DdB8DbN2vEFoGe88P0P3hydQ3AkdVjDd2GFIY3hkNY_7WKJ1cWua04v-w7spz3NuzsmGsXo-1vw=s0-d)
![Range = [0,\pi ] - \left\{ {\frac{\pi }{2}} \right\}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_slK1qMqRF8NYkGdiUlhw6o_Yc2Hu_4JFFzUggXg9h2dc3S8xKLTplvoiHqtEq-yjVPNVssDbOqkgjBEPxgOgR2ABRtGpHlZdGr4be5Sx09YOiycwgaMOHMkX1s2QZFStTIyFsjM8k9T3Xw2fEmapqNBRZID46ZvYDaHHl9kf2gN_aGkoTiSmxqh9FwtAELUEI_ii150xzNyks5F6OK7AUcCG-OTtaODGpt8Ealau7ImHQIKyUeaHjt5tEYHdRmGHbzNdxGc_mNgm_R-XaMS0NZ=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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