# Sketching the graph of trigonometric functions involving absolute value function

How do I sketch the graph of $\tan |x|?$

I know that the modulus over $|x|$ can be thought of as the angle (in radians) will always be positive which implies that the angle is always measured anti-clockwise. But I seem to get no idea about sketching it correctly.

I know how a graph changes when we put absolute value function. Also I don't have any texts that explains such graphs.

Any reference from the web to learn such graphs are welcome.

Kindly help.

## 3 Answers

First, draw the graph for $x>0$. This will be the same graph than $\tan x$. Then, since $\tan |-x|=\tan |x|$, the graph of the function will be symmetric w.r.t the axis $x=0$. Hence, you can draw the part $x<0$ just by using the symmetry of the function.

Hint $f(-x)=f(x)$ so that's an even function. So we know the graph of $tan(x)$ for positive $x$ . Repeat the same graph in negative x axis. Note that the function is symmetric about Y-axis.

Draw or plot together on same graph sheet

$$y= \tan x,(x>0) ,\, y= - \tan x, (x<0)$$

The graph lines have symmetry about y-axis. It is an even function, even or mirrored about y-axis with a slope discontinuity at the origin. In fact if you hold up a mirror on y-axis and look at the real graph and virtual image you can see the full graph.