Question

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

tanB = `(8)/(15)`

Answer 1

tanB = `(8)/(15)`

tanB = `"Perpendicular"/"Base" = (8)/(15)`

By Pythagoras theorem, we have
(Hypotenuse)² = (Perpendicular)² + (Base)²
(Hypotenuse) = `sqrt(("Perpendicular")^2 + ("Base")^2`
= `sqrt((8)^2 + (15)^2`
= `sqrt(64 + 225)`
= `sqrt(289)`
= 17

cot B = `(1)/"tan B" = (15)/(8)`

sin B = `"Perpendicular"/"Hypotenuse" = (8)/(17)`

cos B = `"Base"/"Hypotenuse" = (15)/(17)`

sec B = `(1)/"cos B" = (17)/(15)`

cosec B = `(1)/"sin B" = (17)/(8)`.