Thread: Tangent and secants

Why is the trig function called tangent and secant, A tangent is a line that intesects a circle in exactly one location and a secant intersects a circle in two locations why do the trig functions have these names?

Originally Posted by algebraisabeast

Why is the trig function called tangent and secant, A tangent is a line that intesects a circle in exactly one location and a secant intersects a circle in two locations why do the trig functions have these names?

Take a look at the attached image (click for a bigger version). This is the unit circle, and you can see that the tangent of the angle is the length of a segment of a line that is tangent to the circle. The secant is named as such because "it cuts the circle, and the word 'secant' comes from the Latin word meaning 'cutting'" (from Dave's Short Course in Trigonometry: Right Triangles).