In the 16th century Europe, when decimal point has yet to be developed, Viete(1540-1603) tried to examine trigonometric function analytically.




                
                
                
                
In this equation, let , then, we get:

Thereafter, this equation was widely used in Europe as a method to simplify multiplication in the field of astronomical calculations.

For instance, say is 10,000, and prepare respective angular representation tables for the case of changing from 1 to 10,000, and changing from 1 to 10,000 as well. For angular measures, a sexagesimal system of angular measure (Examples: 98°25´40´´) must have been used, but we shall employ a sexagesimal system of angular measure inclusive of decimal point(Example: 98´.427777). In Europe those days, tables up to 12 digits and 15 digits existed.

Let's calculate as an example.
From the table, let's find angle that makes equal to 4852 and angle that makes equal to 6235. Then, calculate as below:

Look for in the table. If there no exact values are found, and then use those values that are near.

This gives us the value of:

Soon after this, because both Napier (1550-1617) and Briggs (1561-1630) invented common logarithm applicable to multiplication and division, this method was ceased to be used.

Corresponding Table

sin	angle	cos	angle
1	0.005729578	1	89.99427042
2	0.011459156	2	89.98854084
3	0.017188734	3	89.98281127
4	0.022918312	4	89.97708169
5	0.028647891	5	89.97135211
6	0.03437747	6	89.96562253
7	0.040107049	7	89.95989295
8	0.045836628	8	89.95416337
9	0.051566209	9	89.94843379
10	0.057295789	10	89.94270421
11	0.06302537	11	89.93697463
12	0.068754952	12	89.93124505
13	0.074484534	13	89.92551547
14	0.080214118	14	89.91978588
4852	29.02557669
		6235	51.42782406
9990	87.43744127	9990	2.562558733
9991	87.5689636	9991	2.431036405
9992	87.708016	9992	2.291983997
9993	87.85606316	9993	2.143936842
9994	88.01511672	9994	1.984883276
9995	88.18807286	9995	1.811927138
9996	88.37937661	9996	1.620623393
9997	88.59651067	9997	1.403489331
9998	88.85406531	9998	1.14593469
9999	89.18970856	9999	0.810291437

Total(1997)  Today  Yesterday

Japanese sites Mathematical Formulas| Kodawari House| Pinpoint StreetView| Excel VBA Techniques| Excel Formula Analysis|