Why is the trigonometric function tan(x) called the tangent function?

Click on the blue point A. As you trace along the curve the tangent line to point A changes. What is the slope of that tangent line? Next consider how the angle formed by the tangent line and the x-axis is changing as you trace along the curve.
Trace point A until you get a 45 degree angle, you may use the arrow keys on the keyboard. What is the slope of the tangent line at 45 degrees? What is
tan(45) =
Now trace until you get to a 30 degree angle. What is the slope of the tangent line? What is tan(30)?
Why is the trigonometric function tan(x) called the tangent function? Explain