Why??

AIEEE Sample Questions › Fundamentals questions › Why??

I was going through Play with graphs.

There the graph of \sin^{-1} sinx is given .

Though the graph happens to be okay.
I got one problem.
IT SUGGESTS students to learn defination of it

like
x+2Î ; -5Î /2<= x<= -3Î /2
-Î -x ; -3Î /2<=x<= -Î /2

y=\sin^{-1} sinx = x ; - Î /2<=x<=Î /2
Î -x ; Î /2<=x<=3Î /2
and so on.

My doubt is how are we getting this particular defination.
Please help

#Mathematics #Fundamentals

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4 Answers

1

rohna ·2011-04-26 06:44:16

sorry who?

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1

kamalendu ghosh ·2011-04-26 07:03:37

dekh eibhabe inverse trigonometry r sums koris....(doing these after a loong time so pardon me if am wrong)....

case I:
sine^-1sine(x)=x ;-âˆ©/2â‰¤xâ‰¤âˆ©/2

case II
when Î /2<=x<=3Î /2

add or subtract suitably so that we bring a region within -âˆ©/2 andâˆ©/2....

here let us subtract -âˆ©...

-âˆ©/2â‰¤x-âˆ©â‰¤âˆ©/2 but sine(x-âˆ©)=-sinx so we instead multiply by -1 andtake..
-âˆ©/2â‰¤âˆ©-xâ‰¤âˆ©/2 check sine (âˆ©-x)=sinx

case III:

-5Î /2<= x<= -3Î /2

add 2âˆ©
-âˆ©/2â‰¤x+2âˆ©â‰¤âˆ©/2 sine(x+2pi)=sine x

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kamalendu ghosh ·2011-04-26 07:11:14

case IV

-3Î /2<=x<= -Î /2
add pi...

we get -.5 piâ‰¤x+piâ‰¤.5pi

but then sine(x+pi)=-sine x

so we multiply both sides by -1
-.5piâ‰¤-x-piâ‰¤.5x

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49

Subhomoy Bakshi ·2011-04-26 14:05:52

yo kamalendu da! :D

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