This picture shows an animation of the tangent function and its relation to the unit circle. The function y=tan(t) is related to the unit circle in the following manner: The angle t (blue angle measure) is the t coordinate in the ordered pair (t, tan(t)). The value of the tangent is the slope of the red line connecting the origin to the point (cos(t),sin(t)), or you can think of it as the slope of the terminal side of angle t in standard position. The function is π periodic.