First notice the unit circle has a radius of 1. Click and drag the slider for α. Note the size of α in degrees and in radians. (Although we wrote the word radians, it should NOT be written. There is no unit with radians.) The ANGLE α is on the x-axis. The ANGLE α is the LENGTH OF THE ARC in the unit circle for the angle α in degrees. Read this sentence until you understand it. It is critical. The value of the tangent function of the angle α is the [color=#008080]height[/color] of triangle divided by the [color=#800080] width[/color] of the triangle, i.e. the [color=#008080]y-coordinate of T[/color] divided by the[color=#800080] x-coordinate of T[/color].

Rounded to 3 decimal places, how much is α=[math]\frac{\pi}{3}[/math]? What is the α in degrees? Which is on the x-axis of the function in the graph above? Rounded to 1 decimal place, how much is α=[math]\frac{\pi}{4}[/math]? What is the α in degrees? Which is on the x-axis of the function in the graph above? What is the ratio of the y-coordinate to the x-coordinate of the point T when α=[math]\frac{\pi}{4}[/math]? So what is [math]\tan(\frac{\pi}{4})[/math]? Find this point on the graph of the function. What is a decimal approximation for the coordinates of this point? Can you see that the scale of the graph is 1:1? (I use the points (0,0), (0.75,1) and (1.5,∞) as my approximation when drawing the first half cycle of tan(x). Can you see why?)