Question

Any one knows how to solve sin^-1 y = cos y ? (Not using Computer) Mathematically ?

Answer 1

1/sin = cos -> 1= sin cos

But cos^2 + Sin^2 = 1

Equate, u have a quadratic in Sin or Cos.

Answer 2

?

Answer 3

I mean Ssin Inverse !

Answer 4

you want \[\arcsin(y)=\cos(y)\]

I see no way of doing this without some numerical method

Answer 5

Ah, sorry, thought you meant reciprocal which evidently has no solution (not real ones , anyway).

Answer 6

sure...as \[1=\sin(\theta)\cos(\theta)\]

\[\Rightarrow 2=2\sin(\theta)\cos(\theta)\]
\[\Rightarrow 2=\sin(2\theta)\]

which is a problem since \[-1\leq\sin(2\theta)\leq1\]

:)

Answer 7

No,I 'm talking about sin Inverse = Cosine

Answer 8

We know...see my second response.

Answer 9

No That's wrong

Answer 10

what is wrong?

Answer 11

how is sin(x)cos(x)=1 ? For all x ? Just take some values for x as 45 then sin(45)xcos(45)=1/2

Answer 12

see my 2nd response!..not my 3rd which wasn't directed at you

Answer 13

i.e. you want
\[\arcsin(y)=\cos(y)\]
I see no way of doing this without some numerical method

Answer 14

You see no way of doing it ? Ok !

Answer 15

it is not possible...Mathematica can't even solve it exactly. It only gives a numerical solution