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 [math]\displaystyle{ \operatorname{Sin} \theta }[/math] stand for the historical sine, and [math]\displaystyle{ \sin \theta }[/math] stand for the modern sine function,

[math]\displaystyle{ \operatorname{Sin} \theta = R \sin \theta, }[/math]

where [math]\displaystyle{ R }[/math] is the sinus totus, [math]\displaystyle{ R = \operatorname{Sin} 90^\circ. }[/math]

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 Gupta, Radha Charan (2019). Ramasubramanian, K.. ed. 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. https://hal.science/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.