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

Did you know that the function \( h(x) = 6 \cos(5x) \) represents a wave that oscillates between 6 and -6? The "6" is known as the amplitude, showing us how far the wave stretches vertically from its midline (which is at y=0). The frequency, thanks to the "5" multiplying \( x \), means this wave completes 5 cycles in a \(2\pi\) interval, making it quite a peppy oscillation! In practical terms, such cosine functions are everywhere in real life! They're key for modeling various phenomena, such as sound waves, light waves, and even the motion of pendulums. Engineers and scientists use trig functions like this to analyze periodic patterns, ensuring everything runs smoothly in systems like audio equipment, automotive movements, and even in predicting astronomical events!