Trigonometrical Ratios — Formula Sheet

sin A = perpendicular / hypotenuse = BC/AC

cos A = base / hypotenuse = AB/AC

tan A = perpendicular / base = BC/AB

cot A = base / perpendicular = AB/BC

sec A = hypotenuse / base = AC/AB

AC^2 = AB^2 + BC^2

sin A = 1/cosec A

cos A = 1/sec A

tan A = 1/cot A

tan A = sin A / cos A

cot A = cos A / sin A

When AC = 13 and AB = 5 in a right triangle, BC = 12 using Pythagoras theorem.

For that triangle, sin A = 12/13, cos C = 12/13, tan A = 12/5, and cosec C = 13/5.

For the same triangle, sec^2 A - tan^2 A = 1.

In a triangle ABC with AP perpendicular to BC, if cot B = 4/3 and cot C = 12/5, then AP = 30 cm when BC = 112 cm.

In a rhombus ABCD with AC = 18 cm, OA = OC = 9 cm because diagonals of a rhombus bisect each other.