Inverse Trigonometric Functions: A Real-Life Application?

📌 CONCEPT: Inverse trigonometric functions are used to determine the angle of elevation in real-life applications, such as a camera's viewfinder, by reversing the trigonometric ratios to find the angle from the given values.

📐 RULE / FORMULA: The inverse trigonometric function used here is the inverse tangent (arctan) which is denoted as tan^(-1) or arctan(x) = y, where x is the ratio of the opposite side to the adjacent side and y is the angle of elevation.

💡 WORKED EXAMPLE: To determine the height of a building from a distance of 20 meters with an angle of elevation of 60 degrees, we can use the inverse tangent function: tan(60°) = height / 20. Solving for height, we get height = 20 * tan(60°) = 20 * √3 ≈ 34.64 meters.

⚠️ COMMON MISTAKE: Students often forget to check the range of the inverse trigonometric function, which can lead to incorrect results. For example, if the angle of elevation is 120 degrees, the inverse tangent function will not give the correct result, as the angle is outside the range of the arctan function.