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 Problem: If sin(x)=5/13 then find others [ Calculator, Method and examples ]Solution:Your problem -> If sin(x)=5/13 then find otherssin(x)=5/13Opposite side (a), adjacent side (b) and hypotenuse (c)sin(x), cos(x), tan(x) fromulasin(x) = "opposite"/"hypotenuse" = a/ccos(x) = "adjacent"/"hypotenuse" = b/ctan(x) = "opposite"/"adjacent" = a/bcsc(x) = "hypotenuse"/"opposite" = c/asec(x) = "hypotenuse"/"adjacent" = c/bcot(x) = "adjacent"/"opposite" = b/asin(x) = "opposite"/"hypotenuse" = a/c = 5/13Here a=5 and c=13In triangle ABC, by Pythagoras' theoremc^2 = a^2 + b^2:. b^2 = c^2 - a^2= 13^2 - 5^2= 169 - 25= 144:. b = sqrt(144) = 12So, a=5,b=12 and c=13(1) sin(x)=a/c=5/13(2) cos(x)=b/c=12/13(3) tan(x)=a/b=5/12(4) csc(x)=c/a=13/5(5) sec(x)=c/b=13/12(6) cot(x)=b/a=12/5Second Methodsin(x)=5/13(1) cos^2(x)=1-sin^2(x)=1-(5/13)^2=1-25/169=(169-25)/169=144/169:.cos(x)=sqrt(144/169)=12/13(2) tan(x)=sin(x)/cos(x)=(5/13)/(12/13)=5/12(3) csc(x)=1/sin(x)=1/(5/13)=13/5(4) sec(x)=1/cos(x)=1/(12/13)=13/12(5) cot(x)=1/tan(x)=1/(5/12)=12/5

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