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WebGraphing.com Forum » List all forums » Forum: Precalculus and Trigonometry Homework Help » Thread: Restricted domain of Cot x |
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Total posts in this thread: 3 |
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sirt
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Hi, I'm Chris Lee. I'm just curious about arccot (x) graph in this site. Is arccot (x) graph in this site correct? because I saw some other looking graph. the arccot (x) graph in this site has RANGE of (-?/2,0)?(0,?/2] but many other sites shows RANGE of arccot (x) is (0,?) Sorry to bother you, but please answer my question as soon as possible. Thank you Kind Regards, Chris Lee |
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pskinner
Joined: Apr 2, 2005 Posts: 797 Status: Offline |
Chris, That's a good question. Literally speaking, the inverse of a function is the curve you get when you swap x and y (rotate the graph about the line y=x. When it comes to the trig functions, the inverse is not a single-valued function, so some decision needs to be made as to what piece will be used. Here, the concept of the principal value of a function comes in. It is a matter of deciding what piece of the inverse one wants to use as the single-valued portion that gives all the values needed to provide an inverse. For arc sine, arc cosine, and arc tangent, there are no controversies as to what should be taken. However, there is a lack of uniformity for all the other inverse trig functions. So, in the case of arc cot, some take the range to be from (0,pi) while others, like webgraphing.com, take (-pi/2,0) and (0,pi/2]. The rationale in the latter case is to take the largest interval on which the cot is 1-1 that includes x=0. This is the strategy for the other two inverse trig functions, arc sec and arc csc. The rationale for the alternative is to take the largest connected piece of the curve. So, in short, there are really two conventions. In a sense, the question of correctness is not at issue. One can choose either range in the definition for the principal value of arc cotangent. ---------------------------------------- Principal Skinner |
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sirt
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Thank you so much for answering my question during your busy time! |
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Re: Restricted domain of Cot x