How to define a tangent line; how to determine the angle a radius to a tangent forms.
How to define the tangent function for all angles.
How to evaluate the tangent of 3*pi/4.
How to find the length of tangent segments drawn to a circle from the same point.
How to restrict the domain of tangent so it will have an inverse function.
How to define the tangent ratio and identify the tangent of an angle in a right triangle.
How to graph y = tan(theta) for 0 <= theta < pi/2.
How to prove that an angle inscribed in a semicircle is a right angle; how to solve for arcs and angles formed by a chord drawn to a point of tangency.
How to graph y = tan(q) for one or more periods.
How to find the x-intercepts and vertical asymptotes of the graph of y = tan(q).
How to find the angle of inclination of a line.