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

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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

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