Q:

Good book on advanced trig

Is there a good book on trig that covers the geometry of the trig functions and how they relate to waves and SHM.  I've already taken calculus, so I'm looking for more of a Trig 2 type book -- if such a thing exists.
Another interesting topic a Trig 2 book might cover (and that I'd be interested in) is trigonometry in non-Euclidean spaces: spherical trig, hyperbolic trig, etc.

A:

The non-standard trig books I know of are:
Trigonometry by Israel M. Gelfand and Alexander Shen

This might be too low level for you now, but it's cheap and worth taking a look at anyway.

Elementary and Advanced Trigonometry by Kenneth Sielke Miller and John Breffni Walsh

This is probably the best fit for you in my opinion, but the book is not in many libraries, so to look at a copy you'll probably have to either buy it or use interlibrary loan. (UPDATE about 4 years later --- I was was searching to see whether a print copy of this book exists for purchase, and I discovered that a digital copy of the book is now freely available.)

Advanced Trigonometry by Clement Vavasor Durell and Alan Robson

A bit more advanced than Miller/Walsh, plus the emphasis is on pure mathematics whereas Miller/Walsh is more suited for an upper level engineering student. (UPDATE about 4.5 years later --- FYI, there is a 380-page solutions manual for this book, the details of which I posted here.)

A Treatise on Plane and Advanced Trigonometry by Ernest William Hobson

This is more advanced than Durell/Robson, and is also directed mainly towards pure mathematics.

