What Are the Limit Points of the Set {sin(n): n a Positive Integer}?

[cragar]

Homework Statement

a)Determine at least three limit points for the set {sin(n): n a positive integer}
b)How many limit points does the set {sin(n): n a positive integer} have?

The Attempt at a Solution

For a it seems that it wouldn't have a limit point because sin(n) would not converge to anything. On the other hand maybe its obvious and maybe 3 limit points would be
sin(1), sin(2), sin(3) , now that I think about it, it seems like a tricky question.
for part b, if sin(n) has 3 limit points then it seems like the set would have an infinite amount of points.

 

[aeroplane]

From http://en.wikipedia.org/wiki/Limit_point we have that x is a limit point of A={sin(n): n a positive integer} if every neighborhood of x has another element of A different from x. So if you can show that you can approximate x as closely as you wish with elements taken from A, then you have a limit point there. I think three natural points to try to show are limit points are 0,1,-1.

 

[cragar]

so really and point in [-1,1] should be a limit point because i can get as close as I want to any point in there with the sin(n), can points in my set {sin(n)} where n is a natural number.
be a limit point?