Have you ever wondered why the tangent trigonometry function is called a "tangent?" This applet shows where that name comes from. Move the blue point; the length of the red segment is the tangent of the red angle. Also note that the length of segment OC is the secant.
Some questions to think about: What happens to the tangent when [math]\theta[/math] is near 90 or 270? Why? When is the tangent positive? Negative? Zero? When is the absolute value of the tangent less than 1? Greater than 1? Equal to 1? What is the period of the tangent function? What is the relationship between the Length of BC and the slope of OC? Why?