The tangent --- represented as "tan" in shorthand --- is one of the six functions. The tangent angle is computed by dividing the opposite side over the adjacent side in a right triangle. The term "tangent" (or "tangent line") also refers to a line that crosses a circle or curve at exactly one point.
In contrast to a tangent, a secant line passes through exactly two points on a curve or circle. The closer the two points are, the more the secant line resembles a tangent. A secant line is related to a chord, which is a line segment inscribed within the circle that intersects two points.
Two secant lines that meet at a point outside the circle will form an angle equal in degrees to the arc of the circle bounded by those lines. In contrast, because the tangent and radius are perpendicular, their intersecting angle is 90 degrees. However, if a tangent and secant intersect, the degree value of the intercepted arc (the part of the circle "intercepted" by their lines) is equal to one-half of the angle.
Tangents and secants, understandably, have distinct formulas when radians are involved. Radians are the ratio between the radius and an arc. For tangents, the tangent of an angle equals cotangent (pi/2 - angle). For secants, it is the cosecant (pi/2 - angle).