Question

In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.

tan C = `(5)/(12)`

Answer 1

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)`.