which of the trigonometric ratios has a value that is undefined?

Answer:
[tex]\tan \left(\frac{\pi }{2}\right)[/tex]
Step-by-step explanation:
We know that tan(x) is defined as sin(x)/cos(x):
[tex]\tan \left(\frac{\pi }{2}\right),\\\sin \left(\frac{\pi }{2}\right)=1,\\\cos \left(\frac{\pi }{2}\right)=0,\\\\[/tex]
[tex]\tan \left(\frac{\pi }{2}\right) = 1/0 \\[/tex]
1/0 is undefined as 0 is in the denominator