#### Answer

$\frac{\pi}{2}$

#### Work Step by Step

The tangent function is the sine function divided by the cosine function. Therefore, we need to find a value in which cosine is 0 in order to get an undefined tangent.
Now, the cosine graph passes 0 at $\frac{\pi}{2}$ and $\frac{3\pi}{2}$. Therefore, the least positive value for which cosine is 0 is $\frac{\pi}{2}$.
This means that tan$\frac{\pi}{2}$ can be written as sin $\frac{\pi}{2}$ divided by cos $\frac{\pi}{2}$. Since sin $\frac{\pi}{2}$ is 1 and cos $\frac{\pi}{2}$ is zero, this means that tan$\frac{\pi}{2}$ is $1/0$ which is undefined. Therefore, the least positive value for which the tangent function is undefined is $\frac{\pi}{2}$.