Sketch an angle $\theta$ in standard position such that $\theta$ has the least possible positive measure and the point $(-5,-12)$ is on the terminal side of $\theta$. Then find the exact values of the six trigonometric functions for $\theta$. Choose the correct graph below.

Step 1 ：Sketch an angle \(\theta\) in standard position such that \(\theta\) has the least possible positive measure and the point \((-5,-12)\) is on the terminal side of \(\theta\).

Step 2 ：The point \((-5,-12)\) is in the third quadrant. The angle in standard position that has the least possible positive measure and has this point on its terminal side is the angle formed by the negative x-axis and the line connecting the origin and the point \((-5,-12)\).

Step 3 ：Find the length of the hypotenuse of the right triangle formed by the x-axis, the line connecting the origin and the point \((-5,-12)\), and the line perpendicular to the x-axis passing through the point \((-5,-12)\). This is given by the Pythagorean theorem as \(\sqrt{(-5)^2 + (-12)^2} = 13\).

Step 4 ：Use the definitions of the trigonometric functions in terms of the sides of a right triangle to find their values. The exact values of the six trigonometric functions for \(\theta\) are \(\sin(\theta) = -\frac{12}{13}\), \(\cos(\theta) = -\frac{5}{13}\), \(\tan(\theta) = \frac{12}{5}\), \(\csc(\theta) = -\frac{13}{12}\), \(\sec(\theta) = -\frac{13}{5}\), and \(\cot(\theta) = \frac{5}{12}\).

Step 5 ：\(\boxed{\sin(\theta) = -\frac{12}{13}, \cos(\theta) = -\frac{5}{13}, \tan(\theta) = \frac{12}{5}, \csc(\theta) = -\frac{13}{12}, \sec(\theta) = -\frac{13}{5}, \cot(\theta) = \frac{5}{12}}\)