Question

"Question2
If cosθ =7/25,Find the values of all T-ratios of θ.
Chapter 5 , Trigonometry, Exercise -5 , Page number - 273"

Answer 1

Hey there!
We know that,
cosθ = Adjacent side to theta / Hypotenuse.
Cosθ = 7/25

Hypotenuse = 25
Adjacent side = 7

By Pythagoras theorem,
( opposite side )² = ( Hypotenuse )² - ( adjacent side)²

Opposite side = √ [ 25² - (7)² ]= √ 625-49 = √576 = 24

Now, Trigonometry ratios :

sinθ = Opposite side to theta / Hypotenuse = 24/25

tanθ = sinθ / cosθ = 24/25 ÷ 7/25 = 24/7

cotθ = 1/tanθ = 1/( 24/7) =7/24
secθ = 1/cosθ = 1/(7/25) = 25/7
cscθ = 1/sinθ = 1/(24/25) = 25/24

∴ The trigonometric ratios , sinθ = 24/25 , tanθ = 24/7, cotθ = 7/24, secθ = 25/7, cosecθ = 25/24

Answer 2

cos@=b/h=7/25
by Pythagoras theorem. ...
so p=root Of (25 square-7 square) =24
so
sin@=p/h=24/25
tan@=p/b=24/7
sec@=h/b=25/7
cosec@=h/p=25/24
cot@=b/p=7/24