The tangent of an angle is defined in terms of that angle being one of the angles of a right triangle. In a right triangle the tangent is the ratio of side opposite the angle to the side adjacent to the angle. See the graphic representing the right triangle.
The Tangent function has a vertical asymptote at every (n + 1/2) * `pi` radians; i.e. at ...,-450 degrees, -270 degrees, -90 degrees, 90 degrees, 270 degrees, 450 degrees, ....
Here's a graphical depiction of the tangent kind of drawn on it's side. As the
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