Question

If tan $\theta =\frac{15}{8}$, find the values of all T-ratios of $\theta$

Answer 1

We know that,
tanθ = Opposite side to $\theta$ / Adjacent side to $\theta$
tanθ = 15/8

Adjacent side = 8
Opposite side = 15

By Pythagoras theorem,
( Hypotenuse )² = (Adjacent side) ²+ (Opposite side)²

Hypotenuse =√ ( 8² + 15² ) = √ 64 + 225 = √289 = 17

Now, Trigonometry ratios :

cosθ = Adjacent side to $\theta$/ Hypotenuse = 8/17

sinθ = Opposite side of $\theta$ / Hypotenuse = 15/17

cotθ = 1/tanθ = 1/(15/8) = 8/15
secθ = 1/cosθ = 1/(8/17) = 17/8
cscθ = 1/sinθ = 1/(15/17) = 17/15

∴ The trigonometric ratios ,
cosθ = 8/17 ,
sinθ = 15/17 ,
cotθ = 8/15 ,
secθ = 17/8 ,
cosecθ = 17/15