Name ____________________________________
From Euclid to Spigotry
Assignment 3 (outline 4)
Last modified: September 15, 2004

You can do everything on this piece of paper and hand it in. 
Shown in the diagram to the right
is a triangle created by plotting the
complex number z = 3 + 4i.

1. Specify the values of the trigonometric
functions for the angle q:

sin q =         cos q =              tan q =

cot q =         sec q =              csc q =
2. The complex number z2, if plotted, will lead to an angle 2q.  So will z2/5.  Calculate z2/5, and plot it on the diagram.

Then compute the following:

sin 2q =                        cos 2q =                                    tan 2q =

cot 2q =                        sec 2q =                                   csc 2q =

3. Let z = 5 + i. Calculate z2/2, then calculate z2/26, z4/4, and z4/676. The result should be very close to 1 + i.  On the diagram below, plot ,  z2/26, and z4/676

Suppose that tan q = 1/5.  Using the complex arithmetic that you just carried out, show that
tan 4q is very nearly p/4 radians.  This result is the basis of one of the best methods for approximating p that was ever devised, Machin's formula