[Math] Sketching the graph of trigonometric functions involving absolute value function

graphing-functionstrigonometry

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.

Best Answer

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.

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