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 = , cos A = , tan A = , cosec A = , sec A = , cot A =

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

B = ° -

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.

Chapter 11: Trigonometry