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The historical name of this function is the suversed sine, suversine, or susinus versus, and is abbreviated $\operatorname{suvers}(x)$. (Similarly, the function $1 + \sin(x)$ is called the cosuversine or sucoversine.) The earliest use of this name may be in 1801 by Joseph de Mendoza y Rios.
We see in Gregory and Law's 1862 Mathematics for Practical Men,
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