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

Question

anonymous · Answer

1/sin = cos -> 1= sin cos

But cos^2 + Sin^2 = 1

Equate, u have a quadratic in Sin or Cos.

zarkon · Answer

?

anonymous · Answer

I mean Ssin Inverse !

zarkon · Answer

you want $$\arcsin(y)=\cos(y)$$

I see no way of doing this without some numerical method

anonymous · Answer

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

zarkon · Answer

sure...as $$1=\sin(\theta)\cos(\theta)$$

$$\Rightarrow 2=2\sin(\theta)\cos(\theta)$$
$$\Rightarrow 2=\sin(2\theta)$$

which is a problem since $$-1\leq\sin(2\theta)\leq1$$

:)

anonymous · Answer

No,I 'm talking about sin Inverse = Cosine

zarkon · Answer

We know...see my second response.

anonymous · Answer

No That's wrong

zarkon · Answer

what is wrong?

anonymous · Answer

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

zarkon · Answer

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

zarkon · Answer

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

anonymous · Answer

You see no way of doing it ? Ok !

zarkon · Answer

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