\[ \frac{\sin 210^{\circ} \cdot \cos 150^{\circ}}{\tan \left(-60^{\circ}\right) \cdot \tan ^{2} 330^{\circ}} \] (1) \( \frac{\sin \left(-45^{\circ}\right) \cdot \cos 315^{\circ} \cdot \cos 215^{\circ}}{\sin 305^{\circ} \cdot \tan 750^{\circ} \cdot \tan \left(-300^{\circ}\right)} \) (1) \( \frac{2 \sin 150^{\circ} \cos 325^{\circ}-\sin \left(-55^{\circ}\right)}{\cos 395^{\circ}} \) n) \( \frac{\sin 300^{\circ} \cos \left(-395^{\circ}\right)-\cos 210^{\circ} \sin 235^{\circ}}{\tan 150^{\circ} \sin 775^{\circ}+\cos \left(-30^{\circ}\right) \cos 215^{\circ}} \)

Did you know that angles often tell stories that connect to historical events? For example, the famous angle of 210° in your equation represents a point in the unit circle where the coordinates correspond to the coordinates of a position deep into the third quadrant. This relates to classic explorations of the circle and π, which have fascinated mathematicians for centuries. So, when you're working with these angles that seem just number-based, remember they carry a rich history! Now, let's take a trip to the real world! Trigonometric functions used in your expression are crucial in various fields such as engineering and physics. For instance, in physics, they help analyze waves, sound, and light. Understanding these angles aids in calculating things like the angle of elevation or depression, which can be essential in architecture and construction. So, next time you compute a trigonometric expression, remember you might just be designing the future!