Plot the sine and cosine functions

Try this:

import java.awt.BorderLayout;
import java.awt.Graphics;
import java.awt.Polygon;
import java.awt.Color;

import javax.swing.JFrame;
import javax.swing.JPanel;

public class Exercise13_12 extends JFrame {

public Exercise13_12() {
    setLayout(new BorderLayout());
    add(new DrawSine(), BorderLayout.CENTER);
}

public static void main(String[] args) {
    Exercise13_12 frame = new Exercise13_12();
    frame.setSize(400, 300);
    frame.setTitle("Exercise13_12");
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.setLocationRelativeTo(null);
    frame.setVisible(true);

}

class DrawSine extends JPanel {

    double f(double x) {
        return Math.sin(x);
    }

    double gCos(double y) {
        return Math.cos(y);
    }

    protected void paintComponent(Graphics g) 
    {
        super.paintComponent(g);

        g.drawLine(10, 100, 380, 100);
        g.drawLine(200, 30, 200, 190);

        g.drawLine(380, 100, 370, 90);
        g.drawLine(380, 100, 370, 110);
        g.drawLine(200, 30, 190, 40);
        g.drawLine(200, 30, 210, 40);

        g.drawString("X", 360, 80);
        g.drawString("Y", 220, 40);

        Polygon p = new Polygon();
        Polygon p2 = new Polygon();

       for (int x = -170; x <= 170; x++) {
            p.addPoint(x + 200, 100 - (int) (50 * f((x / 100.0) * 2
                    * Math.PI)));

        }

        for (int x = -170; x <= 170; x++) {
            p2.addPoint(x + 200, 100 - (int) (50 * gCos((x / 100.0) * 2
                    * Math.PI)));

        }

        g.setColor(Color.red);
        g.drawPolyline(p.xpoints, p.ypoints, p.npoints);
        g.drawString("-2\u03c0", 95, 115);
        g.drawString("2\u03c0", 305, 115);
        g.drawString("0", 200, 115);

        g.setColor(Color.blue);
        g.drawPolyline(p2.xpoints, p2.ypoints, p2.npoints);

    }
 }
}

Basically it's the same code all over, but you need a new polygon to draw it. And then I set the color using the setColor() function of the Graphics.

You can add this to your paintComponent method:

        //Draw pi and -pi
        g.drawString("-\u03c0", 147, 100);
        g.drawString("\u03c0", 253, 100);   

        //Create a new polygon
        Polygon p2 = new Polygon();

        //Add the points of the cosine
        for (int x = -170; x <= 170; x++) {
            p2.addPoint(x + 200, 100 - (int) (50 * g((x / 100.0) * 2
                    * Math.PI)));
        }
        //Draw the function
        g.drawPolyline(p2.xpoints, p2.ypoints, p2.npoints);

With that you can have the results that you need.