Question

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

cosec C = `sqrt(10)`

Answer 1

cosec C = `sqrt(10)`

cosec C = `(1)/"sin C" = "Hypotenuse"/"Perpendicular" = sqrt(10)/(1)`

By Pythagoras theorem, we have
(Hypotenuse)² = (Perpendicular)² + (Base)²
⇒ Base = `sqrt(("Hypotenuse")^2 - ("Perpendicular")^2`
⇒ Base
= `sqrt((sqrt(10))^2 - (1)^2`
= `sqrt(10 - 1)`
= `sqrt(9)`
= 3

sin C = `"Perpendicular"/"Hypotenuse" = (1)/sqrt(10)`

cos C = `"Base"/"Hypotenuse" = (3)/sqrt(10)`

tan C = `"Perpendicular"/"Base" = (1)/(3)`

sec C =`(1)/"cos C" = sqrt(10)/(3)`

cot C = `(1)/"tan A"` = 3.