INVERSE TRIGONOMETRY FUNCTION HANDWRITTEN NOTES FOR NDA EXAM 2022 help4nda

 INVERSE TRIGONOMETRY FUNCTION

Inverse of a function ‘f ’ exists, if the function is one-one and onto, i.e, bijective. Since trigonometric functions are many-one over their domains, we restrict their domains and co-domains in order to make them one-one and onto and then find their inverse.

Notes: 

(i) The symbol sin–1x should not be confused with (sinx) –1. Infact sin–1x is an angle, the value of whose sine is x, similarly for other trigonometric functions. 

(ii) The smallest numerical value, either positive or negative, of θ is called the principal value of the function.

(iii) Whenever no branch of an inverse trigonometric function is mentioned, we mean the principal value branch. The value of the inverse trigonometic function which lies in the range of principal branch is its principal value.

Graph of an inverse trigonometric function :

The graph of an inverse trigonometric function can be obtained from the graph of original function by interchanging x-axis and y-axis, i.e, if (a, b) is a point on the graph of trigonometric function, then (b, a) becomes the corresponding point on the graph of its inverse trigonometric function. It can be shown that the graph of an inverse function can be obtained from the corresponding graph of original function as a mirror image (i.e., reflection) along the line y = x.

notes for inverse trigonometry function :-

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NDA MATHEMATICS NOTES :

#COMPLEX NO.

#SET THEORY

#RELATION 

#PERMUTATION AND COMBINATION

#PROBABILITY

#VECTOR

#LOGARITHM

#BINARY NO.

#TRIGONOMETRY

GEOGRAPHY

POLITY

CHEMISTRY

AUXILIARY VERBS

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