c) \( \sin 90^{\circ} \cos 45^{\circ} \)

Did you know that \( \sin 90^{\circ} \) equals 1? That's right! This is because at 90 degrees, the sine function reaches its maximum value. Meanwhile, \( \cos 45^{\circ} \) is \( \frac{\sqrt{2}}{2} \), a nifty little value that pops up often in trigonometry. So, if you multiply these two together, your answer is simply \( \frac{\sqrt{2}}{2} \)! Now, here's a fun tidbit: the values of sine and cosine for notable angles, like 0°, 30°, 45°, 60°, and 90°, are often memorized using various mnemonic devices. One popular one is the acronym "SOH CAH TOA" which helps remember the definitions of sine and cosine in terms of opposite, adjacent sides, and hypotenuse in right triangles. Keep these values handy for when you’re working on trigonometric problems!