If , find all the values of all the trignometeric ratios of θ.

We have, sinθ = = perpendicular/hypotenuse (For some value of k)



By Pythagoras theorem, (hypotenuse)2 = (perpendicular)2 + (base)2


AB2 = BC2 + AC2


{(a2 + b2)k}2 = {(a2 - b2)k}2 + AC2


a4k2 + b4k2 + 2a2b2k2 = a4k2 + b4k2 - 2a2b2k2 + AC2


AC2 = 4a2b2k2 = (2abk)2


AC = 2abk


Hence, the trigonometric ratios for the given θ are:


sinθ =


cosθ = AC/AB = =


tanθ = BC/AC = sinθ /cosθ =


cotθ = AC/BC = 1/tanθ =


cosecθ = AB/BC = 1/sinθ =


secθ = AB/AC = 1/cosθ =


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