Q. 33.9( 15 Votes )

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

Answer :

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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