# If tanθ = 15/8, find all the values of all the trignometeric ratios of θ.

We have, tanθ = 15k/8k = perpendicular/base (For some value of k)

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

AB2 = BC2 + AC2

AB2 = (15k)2 + (8k)2

AB2 = 225k2 + 64k2

AB2 = 289k2 = (17k)2

AB = 17k

Hence, the trignometeric ratios for the given θ are:

sinθ = BC/AB = (15k)/(17k) = 15/17

cosθ = AC/AB = (8k)/(17k) = 8/17

tanθ = 15/8

cotθ = AC/BC = 1/tanθ = 8/15

cosecθ = AB/BC = 1/sinθ = 17/15

secθ = AB/AC = 1/cosθ = 17/8

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