Question

A sound wave is modeled with the equation y=1/4 cos 2pi/3theta. Find the period. Explain your method. Find the amplitude. Explain your method. What is the equation of the midline? What does it represent? Please help and explain this. I don't understand this at all!

Answer 1

You know the period of the cos function is 2π, right? Every 2π that the argument to cos goes through is one complete cycle. You've multiplied the argument by 2π3 so that changes the period. If we had simply multiplied by 2, you would have 2 cycles per 2π change in θ instead of the usual 1, and the period would be correspondingly halved. Can you figure out the new period in your equation? The amplitude is easy to find. The value of cos varies from 1 to -1. You've multiplied it by 1/4. What will that do to the amplitude?