Question

"Question4
If Cot θ=2,Find the values of all T-ratios of θ.
Chapter 5 , Trigonometry, Exercise -5 , Page number - 273"

Answer 1

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

Cot x = base/perpendicular
= b/p = 2 = 2/1
so base and perpendiculars of a right angle triangle is given.
so by Pythagoras theorem.
h^2 = p^2 + b^2
h^2 = 1^2 + 2^2
h^2 = 5
h = √5
there fore,
sin x = p/h = 1/√5
cos x = b/h = 2/√5
cosec x = 1/sin x = √5
sec x = 1/cos x = √5/2
tan x = 1/cot x = 1/2