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Evaluate \csc^{-1} (\sin \frac{1}{9}) ?

Option: 1

6-2\pi


Option: 2

2\pi-6


Option: 3

6


Option: 4

\pi-6


Answers (1)

best_answer

 

 

Graph of Principal Value of function f-1 (f (x)) ((Part 1) -

Graph of Principal Value of function f-1 (f (x)) ((Part 1)

  1. Graph of cosec-1( cosec (x))

Domain of the function is R - {nπ, n ∈ I} and range is [- π/2, π/2] - {0}

            y = cosec-1( cosec (x))

∴          cosec y = cosec x

or         sin x = sin y

Hence, graph of cosec-1( cosec (x)) is the same as that of y = sin-1( sin (x)), but excluding points x =  nπ, n ∈ I.

 

 

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\csc^{-1} (\sin \frac{1}{6})=\csc^{-1} (\csc {6})=y\\ \text{from above graph in concept }\\ y=6-2\pi

Posted by

Irshad Anwar

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