The inverse functions are called the arcsine, arccosine, and arctangent, respectively.
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It is unlikely that any of the geographers could compute the arctangent, or angle of that tangent.
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He developed the concepts of the power series and Taylor series, and produced the power series expansions of sine, cosine, tangent, and arctangent.
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In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and the Taylor series, of functions such as sine, cosine, tangent and arctangent.
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It appears that the most one can argue reasonably is a power series expansion for the arctangent function, exploited to determine pi with substantial accuracy.
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More examples
Arc tangent: the inverse function of the tangent; the angle that has a tangent equal to a given number
In mathematics, the inverse trigonometric functions or cyclometric functions are the inverse functions of the trigonometric functions, though they do not meet the official definition for inverse functions as their ranges are subsets of the domains of the original functions. ...