To find the value of [tex]\(\tan \theta\)[/tex], we need to understand the relationship between the coordinates of the point [tex]\( P \)[/tex] and the tangent function.
The coordinates of the point [tex]\( P \)[/tex] are [tex]\((-3, -4)\)[/tex].
The tangent of an angle [tex]\(\theta\)[/tex] in standard position, where the terminal side of the angle passes through the point [tex]\( P(x, y) \)[/tex], is given by:
[tex]\[
\tan \theta = \frac{y}{x}
\][/tex]
Let's apply this formula to the coordinates given:
[tex]\[
x = -3 \quad \text{and} \quad y = -4
\][/tex]
Now, substitute these values into the formula:
[tex]\[
\tan \theta = \frac{y}{x} = \frac{-4}{-3}
\][/tex]
Simplifying the fraction:
[tex]\[
\tan \theta = \frac{4}{3}
\][/tex]
Therefore, the value of [tex]\(\tan \theta\)[/tex] is:
[tex]\[
\tan \theta = \frac{4}{3}
\][/tex]
So, the correct answer from the given choices is:
[tex]\[
\tan \theta = \frac{4}{3}
\][/tex]
