The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘metron’ and it means ‘measuring the sides of a triangle’. The subject was originally developed to solve geometric problems involving triangles.
It was studied by sea captains for navigation, surveyor to map out the new lands, by engineers and others. Currently, trigonometry is used in many areas such as the science of seismology, designing electric circuits, describing the state of an atom, predicting the heights of tides in the ocean, analysing a musical tone and in many other areas.
Relation between degree and radian: 2π radian = 360° or π radian = 180°
Trigonometric Functions
sin2 x + cos2 x = 1
Domain and range of trigonometric functions
-1 ≤ sin x ≤ 1 and -1 ≤ cos x ≤ 1
Trigonometric Functions of Sum and Difference of Two Angles
cos (x + y) = cos x cos y - sin x sin y
cos (x - y) = cos x cos y + sin x sin y
sin (x + y) = sin x cos y + cos x sin y
sin (x - y) = sin x cos y - cos x sin y
Trigonometric Equations
Equations involving trigonometric functions of a variable are called trigonometric equations. The solutions of a trigonometric equation for which 0 ≤ x < 2π are called principal solutions. The expression involving integer n which gives all solutions of a trigonometric equation is called the general solution.