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I have the following problem :

If $\sec(1.4) = x$, find the value of $\csc(2\tan^{-1}x)$.

(A) $0.33$

(B) $0.87$

(C) $1.00$

(D) $1.06$

(E) $3.03$

I we take the $1.4$ as degrees, we get option (C), if we take it as radians, we get (E). Besides common sense, what other ways do we have to conclude that it the $1.4$ is in radians?

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$\tan^{-1}(x)$ or $\tan^{-1}(1.4)$? –  B. S. May 3 '13 at 9:25
    
It is tan−1(x). –  Hele May 3 '13 at 9:26
    
I'm sorry, i think you dont understand my question. I know how to solve the sum. Please read the question thoroughly. –  Hele May 3 '13 at 9:32
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While I agree this question isn't very well written, I'd think that if these were degrees they would have the little circle next to them. –  Javier Badia May 3 '13 at 9:49
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1 Answer

up vote 2 down vote accepted

Since radians and degrees describe the same concept, just in different denominations, I don't think there is a way to "know" which you're intended to use without being explicitly told.

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So the take-away message is basically that any problem which requires an answer of the format "Angle", does not specify which form of angle the answer should be in, and has multiple-choice responses which fulfill both forms is a badly formulated problem. –  NWard May 3 '13 at 9:34
    
This is an SAT practice question. I'm taking the exam. Thanks for your help :) –  Hele May 3 '13 at 9:37
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That is unfortunate then because as I understand it the SAT is a Scantron-evaluated exam, so whereas a human grader could read your errata statement of "both answers are correct given the form of the answer", the machine will grade you incorrect if you "guess" which one it wants incorrectly. Hopefully the real test will be free of such errors :) Good luck! –  NWard May 3 '13 at 9:40
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