### A good answer might be:

actual x valueX = x * 599/(2*PI)
0.0 0
2*PI 599

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.)

# Linear Equation

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. So we need to map (-1 to +1) to (0 to 399).

actual y valueinteger Y to fit applet width
-1.0 399
+1.0 0

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.*;

// The drawing area is 600 by 400.
// (X=0, Y=0) is the top left corner.
//
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 many other applications. It is well worth the time you spend with it.

### QUESTION 11:

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