Find the remaining trigonometric functions of

Question

iftan(theta)=m/n wheremandnare both positive.

Answer 1

Given that tanθ = m/n = opposite side/adjacent side             

       

where m = opposite side length, n = adjacent side length and √(m^2 + n^2) = hypotenuse

∴ sinθ = opposite side / hypotenuse = m / √(m^2 + n^2)

∴ cosθ = adjacent side / hypotenuse = n / √(m^2 + n^2)

∴ cotθ = adjacent side / opposite side = 1/ tanθ = n/m

∴ cosecθ = hypotenuse / opposite side = 1/ sinθ = √(m^2 + n^2) / m

∴ secθ = hypotenuse / adjacent side = 1/ cosθ = √(m^2 + n^2) / n