To find the value of tan(θ), we need to determine the ratio of the length of the side opposite to the angle (y-coordinate) to the length of the side adjacent to the angle (x-coordinate).
Since the terminal side of the angle passes through P(-3,-4), we can use the coordinates of P to determine the values of x and y. The x-coordinate is -3, and the y-coordinate is -4.
Next, we can find the length of the hypotenuse (r) using the Pythagorean theorem:
r = sqrt((-3)^2 + (-4)^2) = 5
Therefore, the length of the side opposite to the angle (y-coordinate) is -4, and the length of the side adjacent to the angle (x-coordinate) is -3.
Now we can calculate the value of tan(θ):
tan(θ) = opposite/adjacent = (-4)/(-3) = 4/3
Therefore, the value of tan(θ) is 4/3.