### The Magic Calculator and The Sine Addition Formula

Bryan Dorner

Mathematics Department

Pacific Lutheran University

Tacoma, WA 98447

Phone: (253) 535-8737

E-mail: dornerbc@plu.edu

#### ABSTRACT

This paper describes how beginning trigonometry students can compute the sine and cosine
of any angle to any degree of accuracy using only simple geometry and a calculator with
a square root key. The ideas in this algorithm also provide a simple derivation of the
angle addition identity: sin(x+h)=sin(x)cos(h)+cos(x)sin(h).