A good answer might be:

The answers are easy to figure out since multiplication by zero results in zero (at one end) and the (2*PI) in the numberator cancels the (2*PI) in the denominator (at the other end.)

Since the equation is linear, all the points in between will also be correct. Here is the same thing for the integer Y that is needed to graph the function. Recall that the range of sin(x) ( -1 to +1 ) is to be represented in an applet with a height of 400 pixels.

Remember that Y=0 for applets corresponds to the very top row and that Y=399 will be the bottom row. Do this by using another linear equation:

Y =  -y * 399/2 + 399/2

Using these two scaling equations, the scheme for drawing the graph is:

import java.applet.*; import java.awt.*; // assume that the drawing area is 600 by 400 public class sineWave extends Applet { public void paint ( Graphics gr ) { double inc = 1.0/32.0; for ( double x = 0.0; x <= 2*Math.PI; x = x + inc ) { double y = Math.sin( x ); double nextx = x + inc; double nexty = Math.sin( nextx ); int startX = (int)( x * 599/(2*Math.PI) ); int startY = (int)( -y * 399.0/2.0 + 399.0/2.0 ); int endX = (int)( nextx * 599/(2*Math.PI) ); int endY = (int)( -nexty * 399.0/2.0 + 399.0/2.0 ); gr.drawLine( startX, startY, endX, endY ); } } }

This code is not very pretty, I'll admit. However, it is fairly typical code for computer graphics and is well worth the time you spend with it.

QUESTION 11:

Why do the statements say 399.0/2.0 instead of 399/2 ?