The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). trigonometry is the study of relationships between the sides and angles of a triangle.
In a right triangle ABC, right-angled at B,
sin A = side opposite to angle A / hypotenuse
cos A = side adjacent to angle A / hypotenuse
tan A = side opposite to angle A / side adjacent to angle A
cosec A = 1 / sin A
sec A = 1 / cos A
tan A = 1 / cot A
tan A = sin A / cos A
If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined.
The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1.
sin (90° - A) = cos A, cos (90° - A) = sin A
tan (90° - A) = cot A, cot (90° - A) = tan A
sec (90° - A) = cosec A, cosec (90° - A) = sec A
sin2 A + cos2 A = 1
sec2 A - tan2 A = 1 for 0° ≤ A < 90°
cosec2 A = 1 + cot2 A for 0° < A ≤ 90º