Click here for a GSP sketch that allows you to manipulate and see the effects of changing a, b, c, and d, in the function f(x) = a tan(b(xc))+d.
Click here for an applet that generates the tangent graph using the unit circle.
Begin with the first tab at the bottom left of the screen to see the effects of changing a, the second tab to see the effects of changing b, the third tab to see the effects of changing c, the fourth tab to see the effects of changing d, and the last tab to see the big picture.
The Reciprocal Functions
Here is a graph of csc x along with its reciprocal, sin x.
Here is a graph of sec x, along with its reciprocal, cos x.
Here is a graph of cot x, along with its reciprocal, tan x.









































