Inverse Trigonometric Functions: A Real-World Conundrum?

📌 CONCEPT: Inverse trigonometric functions are used to find the original angle in a right-angled triangle, given the ratio of the opposite side to the adjacent side, or the ratio of the opposite side to the hypotenuse.

📐 RULE / FORMULA: The inverse trigonometric functions are denoted by sin^-1, cos^-1, and tan^-1, and they are used to find the angle whose sine, cosine, or tangent is a given value. For example, sin^-1(x) gives the angle whose sine is x.

💡 WORKED EXAMPLE: Suppose the surveyor measures an angle of 36.87° and wants to find the acute angle between the line and the normal to the curve. She can use the inverse trigonometric function calculator to find the angle whose sine is 0.6. Using sin^-1(0.6), she gets an angle of approximately 36.87°. Since the angle is bisected, the acute angle between the line and the normal to the curve is half of 36.87°, which is 18.43°.

⚠️ COMMON MISTAKE: Students often confuse the inverse trigonometric functions with the trigonometric functions, and use the wrong function to solve a problem. For example, to find the acute angle between the line and the normal to the curve, students may use the sine function instead of the inverse sine function.