Given $\tan A=-\frac{12}{5}$ and that angle $A$ is in Quadrant IV, find the exact value of $\sin A$ in simplest radical form using a rational denominator.

Step 1 ：We are given that \(\tan A = -\frac{12}{5}\) and that angle \(A\) is in Quadrant IV. In this quadrant, sine is negative. We also know that \(\tan A = \frac{\sin A}{\cos A}\).

Step 2 ：We can use the Pythagorean identity \(\sin^2 A + \cos^2 A = 1\) to find the value of \(\sin A\).

Step 3 ：By substituting the value of \(\tan A\) into the equation, we can solve for \(\cos A\) and \(\sin A\).

Step 4 ：The value of \(\sin A\) is approximately -0.923. However, the question asks for the exact value in simplest radical form with a rational denominator.

Step 5 ：We can convert this decimal to a fraction and simplify it to get the exact value.

Step 6 ：The exact value of \(\sin A\) in simplest radical form with a rational denominator is \(\boxed{-\frac{12}{13}}\).