CLASS-9
TRIGONOMETRICAL RATIOS - T-RATIOS OF 45⁰
T-Ratios of 45ᵒ -
Consider a ABC in which ∠A = 45⁰, and ∠B = 90⁰, then clearly ∠C = 45⁰.
AB = BC = a (say)
AC = √AB² + BC² = √a² + a²
= √2a² = √2a
BC a 1
sin 45ᵒ = -------- = -------- = -------
AC √2 a √2
AB a 1
cos 45ᵒ = -------- = ------- = ------
AC √2 a √2
BC a 1
tan 45ᵒ = ------- = ------- = ------- = 1
AB a 1
1 1
cosec 45ᵒ = --------- = --------- = √2
sin 45ᵒ 1/√2
1 1
sec 45ᵒ = --------- = ------- = √2
cos 45ᵒ 1/√2
1 1
cot 45ᵒ = --------- = ------ = √2
tan 45ᵒ 1