Question

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

cosB = `(4)/(5)`

Answer 1

cosB = `(4)/(5)`

cosB = `"Base"/"Hypotenuse" = (4)/(5)`

By Pythagoras theorem, we have
(Hypotenuse)² = (Perpendicular)² + (Base)²
⇒ Perpendicular = `sqrt(("Hypotenuse")^2 - ("Base")^2`
⇒ Perpendicular
= `sqrt((5)^2 - (4)^2`
= `sqrt(25 - 16)`
= `sqrt(9)`
= 3

sinB = `"Perpendicular"/"Hypotenuse" = (3)/(4)`

tanB = `"Perpendicular"/"Base" = (3)/(4)`

secB = `(1)/"cosB" = (5)/(4)`

cotB = `(1)/"tanB" = (4)/(3)`

cosecB = `(1)/"sinB" = (5)/(3)`.