Modelling a Ferris Wheel's Height?

📌 CONCEPT: The concept of modelling a Ferris wheel's height involves using trigonometric functions to represent the height of the rider above the ground at any given time.

📐 RULE / FORMULA: The rule/formula that applies here is the given equation h = 10 + 10sin(πt/12), where h is the height of the rider and t is the time in hours.

💡 WORKED EXAMPLE: Suppose the person boards the ride at 8 AM. To find the maximum height, we need to determine the value of t that maximizes the height h. Using the equation, we get h = 10 + 10sin(πt/12). The maximum value of h occurs when sin(πt/12) = 1, which gives h = 10 + 10 = 20 meters. Therefore, the maximum height of the rider is 20 meters.

⚠️ COMMON MISTAKE: A common mistake students make is not considering the period of the sine function, which in this case is 12 hours, and not accounting for the fact that the sine function oscillates between -1 and 1.