Trigonometric Ratios and Identities PDF

The only app you need to prepare for JEE Main JEE Adv. BITSAT WBJEE MHT CET and more... 4.8 50,000+ 2,00,000+...

The only app you need to prepare for JEE Main JEE Adv. BITSAT WBJEE MHT CET and more... 4.8 50,000+ 2,00,000+ Rating on Google Play Students using daily Questions available With MARKS app you can do all these things for free Solve Chapter-wise PYQ of JEE Main, JEE Advanced, NEET, BITSAT, WBJEE, MHT CET & more Create Unlimited Custom Tests for any exam Attempt Top Questions for JEE Main which can boost your rank Track your exam preparation with Preparation Trackers Complete daily goals, rank up on the leaderboard & compete with other aspirants 4.8 50,000+ 2,00,000+ Rating on Google Play Students using daily Questions available  TRIGONOMETRIC RATIOS AND IDENTITIES The word trigonon means a triangle and the word metron means a measurement. Hence trigonometry means the science of measuring triangles. SYSTEMS OF MEASUREMENT OF ANGLES There are three systems for measuring angles 1. Sexagesimal or English system 2. Centesimal or French system 3. Circular system Sexagesimal system : The principal unit in this system is degree (°). One right angle is divided into 90 equal part and each part is called one degree (1°). One degree is divided into 60 equal parts and each part is called one minute and is denoted by (1'). One minute is equally divided into 60 equal parts and each part is called one second (1"). In Mathematical form : One right angle = 90° (Read as 90 degrees ) 1° = 60' (Read as 60 minutes ) 1' = 60" (Read as 60 seconds ) Centesimal system : The principal unit in this system is grade and is denoted by (g). One right angle is divided into 100 equal parts, called grades, and each grade is subdivided into 100 minutes, and each minute into 100 seconds. In Mathematical form : One right angles = 100g (Read as 100 grades) 1g = 100' (Read as 100 minutes) 1' = 100" (Read as 100 seconds) Circular system : In circular system the unit of measurement is radian. One radian, written as 1C, is the measure of an angle subtended at the centre of a circle by an arc of length equal to the radius of the circle. Relation between systems of measurement of angles D G 2C   90 100  TRIGONOMETRICAL RATIOS OR FUNCTIONS Let a line OA make  angle with a fixed line OX and AM is perpendicular from A on OX. Then in right-angled triangle AMO, trigonometrical ratios (functions) with respect to  are defined as follows : Y P B P A sin  = , cos  = , tan  = H H B H H B H P cosec  =. sec  = , cot  = P B P  X O B M Note : (i) Since t-ratios are ratios between two sides of a right angled triangle with respect to an angle, so they are real numbers. (ii)  may be acute angle or obtuse angle or right angle.  Trigonometric Ratios and Identities SIGN OF TRIGONOMETRIC RATIOS (i) All ratios sin  , cos  , tan  , cot  , sec  and cosec  are positive in Ist quadrant. (ii) sin  (or cosec  ) positive in IInd quadrant, rest are negative. (iii) tan  (or cot  ) positive in IIIrd quadrant, rest are negative. (iv) cos  (or sec  ) positive in IVth quadrant, rest are negative. DOMAIN AND RANGE OF A TRIGONOMETRICAL FUNCTION If f : X Y is a function, defined on the set X, then the domain of the function f, written as Domain is the set of all independent variables x, for which the image f(x) is well defined element of Y, called the co-domain of f. Range of f : X Y is the set of all images f(x) which belongs to Y , i.e. Range f = {f(x) Y: x  X }  Y The domain and range of trigonometrical functions are tabulated as follows Trigonometric function Domain Range sin x R, the set of all the real number [–1, 1] cosx R –1  cos x  1    tan x R –  2n  1 ,nI  R  2  cosecx R – n  ,n I R–{x:–1