graphical representation of trig functions I'm currently learning the unit circle definition of trigonometry. I have seen a graphical representation of all the trig functions at khan academy. !enter image description here I understand how to calculate all the trig functions and what they represent. Graphically, I only understand why sin and cos is drawn the way it is. I'm having trouble understand why tangent, cotangent, secant, cosecant are drawn the way they are. Can someone please provide me with some intuitions.

While this figure is elegant in its way, it has a little bit too much going on for the beginning student. ![enter image description here](

Lets start with a simpler figure. ![enter image description here](

Our two triangles are similar. The smaller triangle has side lengths $(\cos x, sin x, 1)$

Multiply all three by the same ratio $\frac{1}{\cos x}$ we will get the side lengths of the similar triangle.

$(1,\tan x, \sec x)$

All of the "co" functions are "flipped" across the line $x=y$

![enter image description here](

Relating these figures to the first one, I will point out that these are congruent triangles.

![enter image description here](