Question

If cotθ =30/16 , find the values of cosecθ and sinθ

Answer 1

Answer:

Hey there!

We know that,

cotθ = Adjacent side to theta / Opposite side to theta

cotθ = 2/1

Adjacent side = 2

Opposite side = 1

By Pythagoras theorem,

( Hypotenuse )² = (Adjacent side) ²+ (Opposite side)²

Hypotenuse =√ ( 2² + 1² ) = √ 5

Now, Trigonometry ratios :

cosθ = Adjacent side to theta / Hypotenuse = 2/√5

sinθ = Opposite side of theta / Hypotenuse = 1/√5

tanθ = 1/cotθ = 1/(2) = 1/2

secθ = 1/cosθ = 1/(2/√5) = √5/2

cscθ = 1/sinθ = 1/(1/√5) = √5

∴ The trigonometric ratios , cosθ = 2/√5 , sinθ = 1/√5 , tanθ = 1/2, secθ = √5/2 , cosecθ = √5 .

Answer 2

Step-by-step explanation:

cottheta = b/p=30/16

h= 34

cosectheta=h/p= 34/16=17/8

sintheta= p/h = 16/34 = 8/17