5.3.2 For what values of \( x \) in the interval \( x \in\left(-360^{\circ} ; 0^{\circ}\right) \) will the identity be undefined.

The identity in question, often related to trigonometric functions, becomes undefined at certain points. In this case, for the tangent function, it is undefined whenever the cosine of the angle is zero. This happens at angles of \( -90^{\circ} \) and \( -270^{\circ} \). So, if you're looking for values in the interval \( x \in (-360^{\circ}, 0^{\circ}) \), both \( x = -90^{\circ} \) and \( x = -270^{\circ} \) will make the identity undefined. Additionally, when you consider the sine and cosine functions, the points where these functions are undefined also play a crucial role. For instance, the tangent function \( \tan(x) = \frac{\sin(x)}{\cos(x)} \) is undefined because it involves division by zero when \( \cos(x) = 0 \). Thus, keeping an eye on these critical values helps navigate the trigonometric landscape efficiently!