CLASS-9
TRIGONOMETRICAL RATIOS - T-RATIOS OF 30⁰
First of all, we have to draw an equilateral △ABC with each side 2a,
Then, ∠A = ∠B = ∠C = 30ᵒ
From A, draw AD ⊥ BC.
In △ADB, in which ∠ADB = 90⁰, and ∠BAD = 30⁰,
Base = AD = √3a, Perpendicular = BD = a, and Hypotenuse = AB = 2a
BD a 1
sin 30ᵒ = -------- = ------- = -----
AB 2a 2
AD √3a √3
cos 30ᵒ = ------- = ------- = ------
AB 2a 2
BD a 1
tan 30ᵒ = ------- = ------ = ------
AD √3a √3
1 1
cosec 30ᵒ = -------- = ------ = 2
sin 30ᵒ 1/2
1 1 2
sec 30ᵒ = --------- = -------- = ------
cos 30ᵒ √3/2 √3
1 1
cot 30ᵒ = -------- = ------- = √3
tan 30ᵒ 1/√3