lol Calculate \( \cos \left(180^{\circ}-150^{\circ}\right) \) without Usi: a calculator.

To solve \( \cos \left(180^{\circ}-150^{\circ}\right) \), we can simplify inside the cosine function first. This results in \( \cos(30^{\circ}) \), since \( 180^{\circ} - 150^{\circ} \) equals \( 30^{\circ} \). The cosine of \( 30^{\circ} \) is well-known to be \( \frac{\sqrt{3}}{2} \). Oh, and speaking of angles, did you know that the unit circle is like a magic tool in trigonometry? It helps not only in finding values for sine and cosine but also gives you insights into their relationships with different angles. It's a great way to visualize how those angles behave in different quadrants! If trigonometry ever leaves you puzzled, try sketching it out! Draw out triangles and label your angles; sometimes, making it visual helps to see connections you might overlook. Plus, remember: the reference angle can save you from a lot of headaches. When dealing with angles larger than \(90^{\circ}\), just think about the corresponding angle in the first quadrant!