To solve $\tan(t - \pi)$, we can use a trigonometric identity for the tangent function. The identity is:

$\tan(t - \pi) = \tan(t)$

This means that the tangent function repeats every $\pi$ radians, so shifting the argument of the tangent function by $\pi$ doesn't change its value except for the sign. In other words:

$\tan(t - \pi) = \tan(t)$

However, the sign of the tangent changes because of the properties of the tangent function in different quadrants. Specifically:

$\tan(t - \pi) = \tan(t) \cdot (-1)$

Given that $\tan(t) = \frac{7}{4}$, we can apply this identity:

$\tan(t - \pi) = -\frac{7}{4}$

Thus, the correct answer is:

$\tan(t - \pi) = -\frac{7}{4}$

Would you like further clarification on how the tangent function behaves with angles involving $\pi$?

Here are 5 related questions to deepen your understanding:

1. How does the tangent function behave in different quadrants?
2. What is the period of the tangent function?
3. Can you find $\tan(t + \pi)$ for any value of $t$?
4. What is the relationship between $\tan(t)$ and $\tan(2t)$?
5. How do other trigonometric functions (like sine and cosine) behave when shifted by $\pi$?

Tip: Tangent has a period of $\pi$, meaning it repeats every $\pi$ radians, but the sign alternates depending on the quadrant!