# Calculating the Trigonometry Tables

## By Bob Shumaker; 2 May 2016

Many of the POWs had graduated from engineering schools, and we had a curiosity about mathematics. Toward the end of the war when we had been placed in large rooms containing fifty or so POWs, we decided to create our own trigonometry tables to an accuracy of four decimal places. A few of us remembered the formula for determining the sine of (a + b) and sine of (a – b) and similarly for the cosine. We also remembered the infinite power series for determining sine (a), which is (a + a3/3! + a5/5! + . . .) and the corresponding formula for cos (a). The “a” in these cases must be in radians, not degrees, so we had to do a conversion.

Using this information we assigned a two-man team to calculate, say, the sine of (1 degree) with a back up two-man team to verify the first team’s accuracy. Another group calculated the data for 2 degrees, and so forth. These calculations were done by scratching on the concrete floor, because we had no pencils or paper. To determine, for example, the data for larger degrees we used the (a + b) formulas. Thus, to get to 5 degrees, we combined the data we had determined for 2 degrees and 3 degrees.

These days, of course, all you need do is to look this information up on a hand held computer. But hand held computers didn’t exist in those days and even if they had existed, we wouldn’t have had access to them. The world has advanced, but the basic knowledge never changes . . . nor does a man’s curiosity.