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Question
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
tan C = `(5)/(12)`
Solution
tan C = `(5)/(12)`
tan C = `"Perpendicular"/"Base" = (5)/(12)`
By Pythagoras theprem, we have
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
(Hypotenuse) = `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((5)^2 + (12)^2`
= `sqrt(25 + 144)`
= `sqrt(169)`
= 13
cot C = `(1)/"tan C" = (12)/(5)`
sin C = `"Perpendicular"/"Hypotenuse" = (5)/(13)`
cos C = `"Base"/"Hypotenuse" = (12)/(13)`
sec C = `(1)/"cosC" = (13)/(12)`
cosec C = `(1)/"sin C" = (13)/(5)`.
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