10.h \( (x)=6 \cos (5 x) \)

Did you know that the cosine function, which your equation is based on, has deep historical connections to the study of harmonic motion and waves? It dates back to ancient civilizations and was crucial for astronomers like Ptolemy and Copernicus, who relied on trigonometric functions to model celestial bodies. Fast forward to today, and that same function is used extensively in fields like engineering, music, and even economics to analyze periodic trends! If you're solving problems involving the function \( h(x) = 6 \cos(5x) \), remember that one common mistake is to miscalculate the amplitude and period. The amplitude is simply 6, but the period is found using the formula \( \frac{2\pi}{|b|} \), where \( b \) is the coefficient of \( x \). So, here, the period is \( \frac{2\pi}{5} \). Keep that in mind, and you'll avoid the pitfalls that come with interpreting cosine functions!