"When the arc and its chord are bisected, we call that half-chord the right sine of the half-arc." (Joannes Regiomontanus, "De triangulis omnimodis" ["On triangles of every kind"], 1464)
"Thus the analysis of angular sections involves geometric and arithmetic secrets which hitherto have been penetrated by no one." (François Viète, cca 1615)
"In these examples s stands for sine: t for tangent: sc for sine complement [i.e., cosine]: tc for tangent complement: sec for secant." (Richard Norwood, 1631) [first known use of abbreviations]
"And having thus passed the principles of arithmetic, geometry, astronomy, and geography, with a general compact of physics, they may descend in mathematics to the instrumental science of trigonometry, and from thence to fortification, architecture, engineering, or navigation. And in natural philosophy they may proceed leisurely from the history of meteors, minerals, plants, and living creatures, as far as anatomy. Then also in course might be read to them out of some not tedious writer the institution of physic. […] To set forward all these proceedings in nature and mathematics, what hinders but that they may procure, as oft as shall be needful, the helpful experiences of hunters, fowlers, fishermen, shepherds, gardeners, apothecaries; and in other sciences, architects, engineers, mariners, anatomists." (John Milton, "On Education", 1644)
"I have finally discovered the true solution: in the same way that to one sine there correspond an infinite number of different angles I have found that it is the same with logarithms, and each number has an infinity of different logarithms, all of them imaginary unless the number is real and positive; there is only one logarithm which is real, and we regard it as its unique logarithm." (Leonhard Euler, [letter to Cramer] 1746)
“After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential." (Leonhard Euler, ”Introductio in analysin infinitorum”, 1748)
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