Question

"Question1
If sin θ =√3/2 ,Find the values of all T-ratios of θ.
Chapter 5 , Trigonometry, Exercise -5 , Page number - 273"

Answer 1

Hey there!
We know that,
sinθ = Opposite side to theta / Hypotenuse.
sinθ = √3/2

Hypotenuse = 2
Opposite side = √3 .

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

Adjacent side = √ [ 2² - (√3)² ]= √ 1 = 1 .

Now, Trigonometry ratios :

cosθ = Adjacent side to theta / Hypotenuse = 1/2

tanθ = sinθ / cosθ = √3/2 ÷ 1/2 = √3/2 * 2/1 = √3

cotθ = 1/tanθ = 1/√3
secθ = 1/cosθ = 1/(1/2) = 2
cscθ = 1/sinθ = 1/(√3/2) = 2/√3

∴ The trigonometric ratios , cosθ = 1/2 , tanθ = √3 , cotθ = 1/√3 , secθ = 2 , cosecθ = 2/√3

Answer 2

sin  θ = √3/2
thus  θ can be 60°
cos  θ = cos 60° = 1/2
tan θ = tan 60° = √3
cot θ = cot 60° = 1/√3
sec θ = sec 60° = 2
cosec  θ = cosec 60° = 2/√3