Question

"Question3
If tan θ =15/8,Find the values of all T-ratios of θ.
Chapter 5 , Trigonometry, Exercise -5 , Page number - 273"

Answer 1

Hey there!
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

Answer 2

Hi.

Here is the answer---

________________

tan θ = 15/8

Refers the attachment for the Questions

We know, the formula of tanθ is Perpendicular/Base.

Thus, Let Perpendicular of the Right angled triangle be 15x and 8x.

Applying Pythagoras Theorem,

          P² + B² = H²
 Thus, H² = 225x² + 64x²
            H²   =  289x²
    ⇒   H = 17x


Now, For the Trigonometric Ratios,

Sinθ = P/H
        = 15x/17x
       = 15/17

Cosθ = B/H
         = 8x/17x
         = 8/17

Cotθ = 1/tanθ
         = 1/(15/8)
         = 8/15

Cosecθ = 1/Sinθ
             = 1/(15/17)
             = 17/15

Secθ = 1/Cosθ
         = 1/(8θ/17)
         = 17/8


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Hope it helps.


Have a nice day.