SOLUTION: hey please help me with this problem,and if possible can you show me the work that leads to the answer. thank you very much
if cot x = 5/12 and cos x > 0 find csc
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Question 600688: hey please help me with this problem,and if possible can you show me the work that leads to the answer. thank you very much
if cot x = 5/12 and cos x > 0 find csc
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
cot(x) = 5/12
cot^2(x) = (5/12)^2
cot^2(x) = 25/144
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Now use the identity 1+cot^2(x) = csc^2(x)
1+cot^2(x) = csc^2(x)
1+25/144 = csc^2(x)
169/144 = csc^2(x)
csc^2(x) = 169/144
csc(x) = sqrt(169/144) ... See note below
csc(x) = sqrt(169)/sqrt(144)
csc(x) = 13/12
Note: Because cos(x) > 0 and cot(x) = cos(x)/sin(x), this means that sin(x) > 0 as well (to keep cot(x) positive). This forces csc(x) > 0 (because csc(x) = 1/sin(x))
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Answer: So the answer is csc(x) = 13/12
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