Evaluating Trigonometric Expressions?

📌 CONCEPT: The height 'h' of the roller coaster can be expressed in terms of the angle 't' using trigonometric functions, specifically the sine function, as the sine of an angle in a right-angled triangle is the ratio of the opposite side (height) to the hypotenuse (distance from the starting point).

📐 RULE / FORMULA: We can use the sine function to express the height 'h' as h = a * sin(t), where 'a' is the maximum height of the roller coaster and 't' is the angle in radians.

💡 WORKED EXAMPLE: Given that the maximum height 'a' is 20 meters, we can express the height 'h' of the roller coaster at any instant 't' as h = 20 * sin(t). For example, if the angle 't' is π/4 radians, the height 'h' would be h = 20 * sin(π/4) = 20 * 0.707 = 14.14 meters.

⚠️ COMMON MISTAKE: Students often forget to consider the maximum height 'a' in the expression h = a * sin(t) or incorrectly calculate the sine of the angle 't'.