# Find the value of ?

1. Apr 5, 2008

### mkbh_10

1. The problem statement, all variables and given/known data

Find the value of sin inverse (2 ) ?

2. Relevant equations

3. The attempt at a solution

This was a question in my final exam & i had no clue about it

2. Apr 5, 2008

### rohanprabhu

is it a real value? what is the domain of the ArcSin function?

3. Apr 5, 2008

### mkbh_10

No extra information was given

4. Apr 5, 2008

### Gib Z

Suppose such a value, k, exists, so that $$\arcsin 2 = k$$. Then taking sines of both sides, $$sin (k) = 2$$. However, the sine function is bounded between -1 and 1 for all real numbers. Hence there is no real solution.

5. Apr 5, 2008

### tiny-tim

… hyperbolic sines … !

Hi mkbh_10! Hope you passed!

Hint: cosh ix = cosx, and sinh ix = isinx.

(that's why sinh is called the hyperbolic sin!)

So sin(x + iy) = sinx cos iy + cosx sin iy = sinx coshy - i cosx sinhy;

so you needed cosx = 0, and … ?

6. Apr 5, 2008

### mkbh_10

But there is no hyperbolic sine function in the question ?

I am studying in DU (Delhi University ) so results will only be out in mid July . I will definitely pass but i want top marks which i will not be getting in this paper coz of my silly mistakes .

7. Apr 5, 2008

### HallsofIvy

Staff Emeritus
What course is this for? That's important. If you are studying complex numbers in the course, then there is a solution, if not, there is no solution.

And just because there is no "hyperbolic sine" in the problem doesn't mean you can't use one to solve it.

8. Apr 5, 2008

### mkbh_10

i have not found it anywhere in my course , thats why i am asking , i didn't study this type of question neither did our teacher taught nor does the book has this type of questions

9. Apr 5, 2008

### mkbh_10

i have studied complex numbers but i have no clue about it

10. Apr 5, 2008

### tiny-tim

… really unfair … !

That's really unfair!

(even if you've done things like log(-1) and log(i), sin(ix) isn't obvious, and should have been pointed out to you, IMO)

(Check the official syllabus, to see if it's on it … if it's not, complain about the exam … if it is, check with your fellow students, and make a joint request for credit for that question … will your student union help you with that?)

(btw, sin (π/2 - isinh^(-1)2) = 2)

11. Apr 5, 2008

### mkbh_10

this is india, nothing happens at student level , & there are 30-40 clgs in DU that have this course & who knows what teacher teaches in a particular topic

12. Apr 5, 2008