Trigonometric Ratios Of Complementary Angles

Two angles are said to be complementary if the sum of their angles is 90^o. In triangle ABC, the pair of complementary angles are

So ∠A + ∠B = 90^o

sin A = BCAB , cos A = ACAB , tan A = BCAC , cosec A = ABBC , sec A = ABAC , cot A = ACBC

Let us now define trigonometric ratios for angle B in terms of it's complementary angle.

B = 90^o - A

So sin B = sin(90 - A) = ACAB. But ACAB is nothing but

cos C = cos (90-A) = BCAB =

tan C = tan (90-A) = ACBC=

sin(90-A) = cos A cosec(90-A) = sec A

cos(90-A) = sin A sec(90-A) = cosec A

tan(90-A) = cot A cot(90-A) = tan A

Note : tan 0° = = cot 90°, sec 0° = = cosec 90° and sec 90°, cosec 0°, tan 90° and cot 0° are not defined.

Introduction to Trigonometry