The Magic Calculator and The Sine Addition Formula

Students who have grown up with computers and calculators may take their capabilities for granted, but I find something magical about entering arbitrary values and computing transcendental functions such as the sine and cosine with the punch of a button. While the calculation seems like "white magic", the calculator operates like a "black box" we don’t teach our trigonometry students what happens inside. They must trust technology without knowing how it works or how they can independently check the results. However, this talk shows beginning trigonometry students can compute the sine and cosine of any angle to any desired degree of precision using only simple geometry and a calculator with a square root key.