Question

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

cos A = `(7)/(25)`

Answer 1

cos A = `(7)/(25)`

cosA = `"Base"/"Hypotenuse" = (7)/(25)`

By Pythagoras theorem, we have
(Hypotenuse)² = (Perpendicular)² + (Base)²
⇒ Perpendicular = `sqrt(("Hypotenuse")^2 - ("Base")^2`
⇒ Perpendicular
= `sqrt((25)^2 - (7)^2`
= `sqrt(625 - 49)`
= `sqrt(576)`
= 24

sinA = `"Perpendicular"/"Hypotenuse" = (24)/(25)`

tanA = `"Perpendicular"/"Base" = (24)/(7)`

secA = `(1)/"cosA" = (25)/(7)`

cotA = `(1)/"tanA" = (7)/(24)`

cosecA = `(1)/"sinA" = (25)/(24)`.