Find the exact value of \( \cos \left(-45^{\circ}\right) \)

Did you know that the cosine function is an even function? This means that \( \cos(-\theta) = \cos(\theta) \). So, when you're asked to find \( \cos(-45^{\circ}) \), you can simply use \( \cos(45^{\circ}) \), which is a well-known angle in trigonometry. Now, to find \( \cos(45^{\circ}) \), recall that it’s part of the special angles where \( \cos(45^{\circ}) = \frac{\sqrt{2}}{2} \). Therefore, by our earlier reasoning, \( \cos(-45^{\circ}) = \cos(45^{\circ}) = \frac{\sqrt{2}}{2} \). So, there you have it—the exact value is \( \frac{\sqrt{2}}{2} \)!