[I don't know your current knowledge-level of Java or ComputerScience in
general. Therefore some of the hints below may or may not seem trivial
to you.]

Some facts to know beforehand:
(*) In Java the origin (x=0,y=0) is in top-left corner.
    x runs to the right, y runs to the bottom.
(*) In Java Math.sin(...) expects the angle in radians, not in degrees.

For convenience I quote the Java code from
<http://www.javaworld.com/jw-03-1996/animation/Example4Applet.html> here:
    public void paint(Graphics g) {
    Dimension d = size();
    int h = d.height / 2;
    for (int x = 0 ; x < d.width ; x++) {
       int y1 = (int)((1.0 + Math.sin((x - frame) * 0.05)) * h);
       int y2 = (int)((1.0 + Math.sin((x + frame) * 0.07)) * h);
       g.drawLine(x, y1, x, y2);
    }
    }
and the HTML code
  <applet code=Example4Applet.class width=500 height=50>
    <param name=fps value=10>
  </applet>

A strategy for understanding an algorithm is stepping through it with
pencil and paper (and a desk-calculator for the sine) as if you were the
computer.

(1) In the HTML code above note the applet parameter: fps=10 (by the
way: "fps" probably means "frames per second").

(2) Now look into the complete Example4Applet.java (into method
"init()"). There the "fps" applet-parameter is used to calculate a
variable "delay". You get delay = 20 (Repeat that calculation fo yourself!)

(3) Now look into method "run()" of Example4Applet.java.
There the "delay" variable is used to increment the variable "frame"
(which initially had the value 0) by 1 every 20 milliseconds.

(4) Proceed to method "paint(Graphics)". Now your paper-work begins:
Step through the paint method line by line; do the the calculation of
that line (you remembered to switch your desk-calculator to radians),
write down the calculated value of the variables.
Your sheet of paper might look like this:
  d = Dimension(width=500,height=50)
  h = 50/2 = 25
  frame = 0
  /* 1st iteration of the for-loop */
  x = 0
  y1 = (int)((1.0 + Math.sin((0 - 0) * 0.05)) * 25) = 1
  y2 = (int)((1.0 + Math.sin((0 + 0) * 0.07)) * 25) = 1
  //draw a black line from (x|y1) to (x|y2)
  /* 2nd iteration of the for-loop */
  x = 1
  y1 = (int)((1.0 + Math.sin((1 - 0) * 0.05)) * 25) = (int) 2.25 = 2
  y2 = (int)((1.0 + Math.sin((1 + 0) * 0.07)) * 25) = (int) 2.75 = 2
  //draw a black line from (x|y1) to (x|y2)
  /* 3rd iteration of the for-loop */
  .....