Inverse Trig Functions: A Real-World Application?
A manufacturer uses a machine that operates at a speed proportional to the sine of an angle between its parts. If the machine's speed is 240 km/h when the angle is 60°, and the manufacturer wants to increase the speed to 300 km/h, what angle should be set to achieve this, assuming the relationship remains the same?
1 Answer
📌 CONCEPT: Inverse Trigonometric Functions are used to find the angle in a right-angled triangle when the ratio of two sides is known.
📐 RULE / FORMULA: The inverse trigonometric function arcsin (or sin^(-1)) is used to find the angle, where arcsin (y) = x, and y = sin(x).
💡 WORKED EXAMPLE: To find the angle when the speed is 300 km/h, we use the inverse sine function: arcsin (5/13) = θ. Using a calculator, we find θ ≈ 75.97°.
⚠️ COMMON MISTAKE: Students often confuse the inverse trigonometric functions with their corresponding trigonometric functions, leading to incorrect calculations.
14 Sept 26
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