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. [br][br]Also note that the length of segment OC is the secant.

Some questions to think about:[br][br]What happens to the tangent when [math]\theta[/math] is near 90 or 270? Why?[br]When is the tangent positive? Negative? Zero?[br]When is the absolute value of the tangent less than 1? Greater than 1? Equal to 1?[br]What is the period of the tangent function? [br]What is the relationship between the Length of BC and the slope of OC? Why?