Name _________________________________
From Euclid to Spigotry
Assignment 5 (outline 6)
Last modified: September 15, 2004
You can do everything on this piece of paper and hand it in.
1. The angles 2p/5, 4p/5, and 0 all have the property that sin 3q = - sin 2q. Draw a diagram to illustrate this fact.  Then use multiple angle formulas to find the quadratic equation satisfied by cos q for q = 2p/5 or 4p/5.   Initially you will have a cubic equation, but you can factor out sin q, thereby losing the solution q = 0.
2. Do the same with sin 4q = - sin q. This time you will get a fourth-degree equation, because an angle of p/3 also has this property. 

3. Richmond's pentagon construction, as illustrated in class and on the Web site, leads to
a pentagon where one vertex is at x = 0, y = 1.  Other constructions give a vertex at x = 1, y = 0.
Redo Richmond's construction so that one vertex is at x = 1, y = 0.  (This is really easy -- just
rotate the diagram through 90 degrees).

4. In the space below, construct a 15 degree angle (p/12 radians).  Find exact expressions, in terms of square roots, for the sine and cosine of p/12  and of 5p/12. For future reference, notice that you have in effect trisected a 45 degree angle.