Sinus totus

In trigonometry, the sinus totus (Latin for "total sine") was historically the radius of the base circle used to construct a sine table; that is, the maximum possible value of the sine.

Letting the notation $\operatorname {Sin} \theta$ stand for the historical sine, and $\sin \theta$ stand for the modern sine function,

$\operatorname {Sin} \theta =R\sin \theta ,$

where $R$ is the sinus totus, $R=\operatorname {Sin} 90^{\circ }.$

References

• Gupta, Radha Charan (1977). "Indian values of the sinus totus". Indian Journal of History of Science Calcutta. 13 (2): 125–143. Presented at the 15th International Congress of History of Science, Edinburgh, 1977. Reprinted in Ramasubramanian, K., ed. (2019). Gaṇitānanda: Selected Works of Radha Charan Gupta on History of Mathematics. Springer. pp. 397–415. doi:10.1007/978-981-13-1229-8_39.
• Roegel, Denis (2021). A survey of the main fundamental European trigonometric tables printed in the 15th and 16th centuries (Report). LORIA (Université de Lorraine, CNRS, INRIA). hal-03330572.
• Van Brummelen, Glen (2021). "1. European Trigonometry Comes of Age". The Doctrine of Triangles: A History of Modern Trigonometry. Princeton University Press. pp. 5, 11, 13, 33. doi:10.1515/9780691219875-002.