If the $\cos$ function is based off of the ratio of the adjacent side of Euclidean, right triangle, with fixed hypotenuse length (such as the unit circle), then how does this correspond to a defined value when $\theta = \pi/2$ ? To me the limit as $\theta \rightarrow 90$ appears to be undefined (specifically 1/0).
Arguments against my view point: 1.) Once you hit 90 for a triangle to exist a new, right triangle will be formed, that is if the hypotenuse is a real number. Counterpoint: That's not the same angle, $\theta$, we used for our original function and when you hit 90 there's not going to be an adjacent side length of zero.
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