You can convert any float or double to an int with a cast. For example:

int integerResult = (int)Math.sin(variable);

However, this really does not make sense. Since the result of Math.sin() will always be from -1 to 1, this cast will always make the result 0 or -1 or 1. From the sound of your question you're not very sure about how to use these. I would strongly recommend you brush up on your math skills before attempting anything too complicated with your programming. You can, of course, use these in floating point format instead of as an integer.

Your second question. 9 * 9 * 9 is equivalent to 9 cubed. You could make your own method for the clearest intent:

int cube(int input) {
    //return the input cubed
    return input*input*input;
}

Or use the built in function Math.pow() like so:

float nineCubed = Math.pow(9,3);

You can see check the java doc to see what functions Java has built in for math.

Finally, you can check out some of these math resources:

What math should all game programmers know?

Linear algebra for game developers part 1

The implementation can be found here^(*).

The sin function is approximated by a 13-degree polynomial. That is, a function on the shape

       c12x¹² + c11x¹¹ + ... + c1x¹ + c0x⁰

on the interval [0,π/4]

The description of the algorithm looks as follows:

33 * Algorithm
34 *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
35 *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
36 *      3. sin(x) is approximated by a polynomial of degree 13 on
37 *         [0,pi/4]
38 *                               3            13
39 *              sin(x) ~ x + S1*x + ... + S6*x
40 *         where
41 *
42 *      |sin(x)         2     4     6     8     10     12  |     -58
43 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
44 *      |  x                                               |
45 *
46 *      4. sin(x+y) = sin(x) + sin'(x')*y
47 *                  ~ sin(x) + (1-x*x/2)*y
48 *         For better accuracy, let
49 *                   3      2      2      2      2
50 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
51 *         then                   3    2
52 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
53 */

^{(*) Disclamer: Talking about OpenJDK here}