## Vineet Loomba is teaching live on Unacademy Plus

INVERSE TRIGONOMETRIC FUNCTIONS FoR SURe SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE) JEE MAIN RANK BOOSTER COURSE PREPARED BY ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SPECIAL ANNOUNCEMENT Share useful links and advice with your learners... CRASH COURSE FOR JEE MAIN 2019 (JANUARY SESSION) Find courses & lessons 735 Courses IIT JEE 2,521 Courses Str Chemistry 797 Courses Details in Plus Tab wwEest HINDI Home My Library Plus Profile SUCCESS IN JEE MAIN ER. VINEET LoOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. * Many of my students are pursuing courses in IITs, NITs, BITs etc unacademy Currently running my own Coaching Institute for JEE Main and Advanced Search vineet loomba unacademy on GOOGLE

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100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) BASICS OF INVERSE FUNCTIONS Let a function f : A B , y : f (x) is such that function is one-one & onto then its inverse exists. Consider a function f : R R , y = sin x, ctions-i- and coda ain Now let the domain o- | and co-domain is [-1, 1] , then its graph becomes thenits f: [-1 ,11+ ,2| y=sin-1 x SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) REMEMBER THIS sin-1 x is not to be interpreted as The sin-1 x is merely a symbol denoting a certain angle whose sine is x. sin X The 1' used in sin-1 x is not an exponent. The inverse trigonometric functions are also written arc sin x, arc cos x etc. 1st quadrant is common to the range of all the inverse functions. 3rd quadrant is not used in inverse function. 4quadrant is used in the clockwise direction i.e. - 2 sys0 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) GRAPHS OF ALL INVERSE TRIGONOMETRIC FUNCTIONS 2' 2 y sin- . T/2 Domain 1,1] Range : [- /2 , /2] Nature one-one y = sin x -t/2-1 y sin x- -1 SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 2. y=c os-1x, 1x1 1, ye[0 , ] -1 Domain : [-1 ,1] Range : [0, ] Nature one-one /y=x y=cos x SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 3. y=tan-1 x , x e R, ye 2'2 Domain R Range (t/2, t/2) Nature one-one = tan x y = tan- x 12 y = tan-x y tan X SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 4, y cot-1x , xeR, ye(0 , ) y A Domain R Range (0, T) Nature : one-one y = cotx1 /2 y = cotx SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) y cosec-1 x , 1 x 1 2 1 , y e 2 Domain Range Nature : (-,-1] [1,0) : [- /2 , /2]-(0) one-one 1 - /2 SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solved Example: Find the principal value of: N3 ) cos-1 /3 Sol: Let be the principal value of cos-1 e [0,n] and cos-| | -| = N3 cos = (ii) 3 Sol: Let 0 be the principal value of tan-1 3 (-2,5) and tan-1W3)- tan --/3 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)