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 =