1. Let's start by understanding what "non-permissible values" of an angle mean in math problems. 2. Non-permissible values are values of the angle that make the expression undefined or invalid. 3. For example, in trigonometry, if you have a function like $\tan \theta = \frac{\sin \theta}{\cos \theta}$, the angle values where $\cos \theta = 0$ are non-permissible because division by zero is undefined. 4. So, non-permissible values are angles that cause division by zero, square roots of negative numbers, or any other invalid operation in the given expression. 5. To find them, set the denominator or the expression inside a square root to values that make the expression invalid and solve for the angle. 6. This helps us restrict the domain of the function to only permissible values where the function is defined and valid.