Why don't tan [math]90^{\circ}[/math] and tan [math]270^{\circ}[/math] exist? - Quora

Answer (1 of 11): What is a "tangent"? It is a line that intersects a circle at only one poimt. Then what is the "TAN" function? It is a function, that returns the slope of the tangent line for a given angle relative to a zero angle. With the "slope" of the tangent line and the point of intersect

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trigonometry - Proving that $\tan \theta=\cot(90^\circ-\theta)$ when $\theta>90^\circ$ - Mathematics Stack Exchange

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How do you tell whether the value of tan 90 degrees is positive