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Given that cot [itex]\theta[/itex] = -12/5 and csc [itex]\theta[/itex] < 0, find sec[itex]\theta[/itex].

This was a question on a test that I drew a blank on, and I'm still not sure how to handle it due to my "teacher" repeatedly dismissing me when I try asking about it. Now, it occurred to me that this could be solved using trig identities and substitution. Starting with [itex]sin^{2}[/itex][itex]\theta[/itex] + [itex]cos^{2}[/itex][itex]\theta[/itex] = 1 and sin/cos = -5/12, I ended up with -

sin = -5/13

cos= 12/13

tan= -5/12

sec= 13/12

and I am confident this is the right answer.But, we have not covered trig identities in class so I am sure there is another easier way to solve this. My question is...what is it? Also, say you take the square root of a trig identity in an equation - how do you know weather it is positive or negative? Thanks in advance.

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# Homework Help: Basic trig test question

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