Find the number of solutions of the equation:

x / 100 = sin x .

the solution 0.

sin 0 = 0

therefore  lhs=rhs

and no other value will satisfy the eqution

the solution 0.

sin 0 = 0

therefore  lhs=rhs

and no other value will satisfy the eqution.

therefore no. of solutions is 1

There are more than one solutions.

let me find out how many..............

The number of solutions won't change even if we rewrite the equation as:

sin[10x]=x/10

here's the graph of this function

this verifies that the answer I derived mathenatically was not correct.

63 is correct but where have I gone wrong!!! 

I found the number of complete loops(15)

but as you can see the 16 th loop also gave two solutions which i did not take into account

so the total no of solutions for x>0 are 31

x<0 are also 31

and x=0 is also a solution

total:63 solutions.

 Not that this sum could not be done without the aid of a computer generated graph.

we could have found the number of halfloops of sin[x] for x<100  (n=[100/pi] =31;[ ]=gif])

then.Now see that the number of halfloops in which sinx is positive is16

so there are 16*2=32 solutions for x>=0.similarly since sinx-(x/100) is odd more 31 solutions exist for x<0total 63 solutions.but even hand drawn graphs will be helpful in this case.............