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What was from a historical point of view the motivation to extend the definition of sin and cos to angles larger than 90 degree?

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  • $\begingroup$ Sine and cosine are ratios of a right triangle, but all triangles in general (right, acute, and obtuse) can still have angles that can be compared to the right triangle, so these ratios remain applicable. $\endgroup$
    – Andrew R.
    Sep 1, 2023 at 22:29
  • $\begingroup$ These are studied in Euclid's Elements, but their study may be dated even earlier. $\endgroup$
    – Andrew R.
    Sep 1, 2023 at 22:35
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    $\begingroup$ That obtuse triangles exist? Once trigonometry was developed they wanted the laws of sines and cosines to apply to them too, for example. Did you mean > 360 degrees? It was the formal attitude of 17th and 18th centuries to extend algebraic manipulations as far and wide as they would bear, compare to Generality of algebra. And the series formulas they had for sin and cos could bear all real, and later even complex, numbers. $\endgroup$
    – Conifold
    Sep 2, 2023 at 5:02
  • $\begingroup$ this a guess: fourier trying to sove PDE using trigonometric series? $\endgroup$ Sep 4, 2023 at 21:14

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