Trig ratios for complementary angles

1. Check whether the angle is written as 90 degrees minus something. 2. Swap sine with cosine or tangent with cotangent as needed. 3. Substitute the known value. 4. Simplify the answer.

Use a right triangle and label the two acute angles A and 90 degrees minus A. The sides opposite one angle become adjacent to the other angle.

A common wrong answer is to keep the same ratio name and only change the angle. That breaks the complementary-angle relationship.

Trigonometric ratios of complementary angles are related by swapping sine with cosine, tangent with cotangent, and secant with cosecant.

Trigonometric ratios of complementary angles are related by swapping sine with cosine, tangent with cotangent, and secant with cosecant. sin(90 degrees - A) = cos A, cos(90 degrees - A) = sin A, tan(90 degrees - A) = cot A, cot(90 degrees - A) = tan A, sec(90 degrees - A) = cosec A, cosec(90 degrees - A) = sec A. sin(90 degrees - A) = cos A and tan(90 degrees - A) = cot A.

Complementary angles add up to 90 degrees. In a right triangle, if one acute angle is A, the other is 90 degrees minus A. Because the two acute angles are complementary, the ratios linked to one angle become the complementary ratios of the other angle. sin(90 degrees - A) = cos A, cos(90 degrees - A) = sin A, tan(90 degrees - A) = cot A, cot(90 degrees - A) = tan A, sec(90 degrees - A) = cosec A, cosec(90 degrees - A) = sec A. If A = 30 degrees, then cos 60 degrees = sin 30 degrees = 1/2. This follows directly from the complementary-angle rule. CBSE may ask you to write the complementary identity, or evaluate a trigonometric ratio using the complementary angle relation. A common wrong answer is to keep the same ratio name and only change the angle. That breaks the complementary-angle relationship.