CLASS-9
TRIGONOMETRICAL RATIOS OF COMPLEMENTARY ANGLES
Trigonometrical Ratios of Complementary Angles –
Two angles are said to be complementary, if the sum of their measures is 90⁰. Thus, A and (90⁰- A) are complementary angles.
T-Ratios of Complementary Angles –
Consider a right angle ABC in which ∠ABC = 90⁰, as shown in the adjoining figure.
So, ∠ACB = (90⁰- A).
Thus, we have –
AB
(i) sin (90⁰ - A) = -------- = cos A
AC
AB
(ii) cos (90⁰ - A) = -------- = sin A
AC
AB
(iii) tan (90⁰ - A) = -------- = cot A
BC
1 1
(iv) cosec (90⁰ - A) = -------------- = ----------- = sec A
sin (90⁰ - A) cos A
1 1
(v) sec (90⁰ - A) = -------------- = ------------ = cosec A
cos (90⁰ - A) sin A
1 1
(vi) cot (90⁰ - A) = ---------------- = ------------ = tan A
tan (90⁰ - A) cot A