Trigonometric ratios of complementary angles
A
B
C
θ
In ΔABC,
∠B = 90º,
…(i)
…(ii)
Hypotenuse
Opposite side
∠A = θ,
∠C = (90 – θ)
90 – θ
∴
sin θ
Adjacent side
BC
AC
BC
AC
=
cos (90 – θ)
sin θ =
cos (90 – θ) =
[From (i) and (ii)]
…(iii)
…(iv)
∴
[From (iii) and (iv)]
Adjacent side
AB
AC
AB
AC
cos θ
=
sin (90 – θ)
cos θ =
sin (90 – θ) =
Opposite side
We know that,
Sum of the measures of all
angles of a triangle is 180°
∴ ∠A + ∠C = 90°
∴ ∠A and ∠C are complementary angles
Trigonometric ratios of complementary angles
A
B
C
θ
In ΔABC,
∠B = 90º,
∠A = θ,
∠C = (90 – θ)
90 – θ
sin θ
=
cos (90 – θ)
cos θ
=
sin (90 – θ)
tan θ
=
cot (90 – θ)
cot θ
=
tan (90 – θ)
cosec θ
=
sec (90 – θ)
sec θ
=
cosec (90 – θ)