Question

Is sin(sin^−1x)= sin^-1(sinx) an identity? Why or why not?

Answer 1

you mean
\[\sin(\sin^{-1}x)\]?

Answer 2

NOPE - it's not

sin inverse of something is always an angle. - can be from -pi/2 to pi/2

BUT sin of something is always a no. that's from -1 to 1.


So, in short, never. ( i mean hardly a few times)

Answer 3

rather 'rarely'

Answer 4

i'd hate to pop your bubble but they're both x :p try calculatoring hehe

Answer 5

arcsine means what number should yoU "sine" to obtain a specific value...let's do numerical

arcsine of 0....what will you sine to get 0? pi/2 will be the answer

now we sine pi/2 which brings us back to 0 so...

\[\sin (\sin^ {-1} 0) = 0\]

let's try the other way around...

\[\sin^{-1} (\sin 0)\]
sin 0 is pi/2

now what is arcsine of pi/2? it's still 0 as welll

@apoorvk :P

Answer 6

Nonsense^

arcsine of pi/2 is NOT -DEFINED - pi is 3.14 so pi/2 is something like 1.57. And in this world, sine can't be greater than one.

Answer 7

sin0 = 0.


Now I know why that ":P" was for.

Answer 8

hm..
\[\sin(\sin^{-1}x)=x\]
\[\sin^{-1}(sinx) =x\]
I think that this what the asker meant.

Answer 9

or girl - 'rini' sounds like a girl.

Answer 10

*facepalm* sin 0 is 1 lol arcsine of 1 is 0 so ha :P

Answer 11

what @Mimi_x3 wrote - those two equations are separately valid - but, they are not the same things.

Answer 12

@lgbasallote you sure you are not confusing 'sine' with 'cosine'?

Answer 13

ARGHHHH SIN 0 IS 0..>ARCSINE OF 0 IS 0..>BOTTTOMLINE THEY ARE EQUAL :PPPP

Answer 14

I always thought they are equal but under certain restriction

Answer 15

arcsin(sin(pi/3)) = 1.0472

sin(arcsin(pi/3)) = 1.5708

so no

Answer 16

i think i forgot something on the calculator tho lol

Answer 17

you cant arcsin pi/3...

Answer 18

pi/3 = 1.4 something.. can't be the value of a sine function

Answer 19

arcsin(sin(7pi/3)) = pi/3

sin(arcsin(7pi/3)) = 7pi/3

http://www.wolframalpha.com/input/?i=sin%28arcsin%287pi%2F3%29%29

Answer 20

well if \(-1 \le x \le 1\) then this is an identity

Answer 21

this is like deriving an integrand equals integrating a derivative

Answer 22

HOW DOES SIN INVERSE OF 7PI/3 EXIST??

pi = 3.14
7pi/3 = around 6.5.

there is an angle for which sine is '6.5'? Amazing - didn't know that!

Answer 23

Wolf just turned into a senseless werewolf. #ProgramsWillBePrograms.

Answer 24

suspend! no one contradicts the great amistre :P lol jkjk

Answer 25

wheres my button lol

Answer 26

the wolf is doing complex things i believe