Inverse Trig Functions: When to Use tan^-1, cos^-1, or cot^-1?

📌 CONCEPT: Inverse trigonometric functions are used to find the angle whose trigonometric ratio is known, and they are denoted by tan^-1, cos^-1, and cot^-1, among others.

📐 RULE / FORMULA: To find the acute angle B in a right-angled triangle ABC, we can use the inverse trigonometric function tan^-1, which is defined as the inverse of the tangent function, i.e., tan^-1(x) = θ, where x = tan(θ).

💡 WORKED EXAMPLE: In triangle ABC, AB = 5 cm and BC = 12 cm. We can use the inverse tangent function to find angle B: tan(B) = AB/BC = 5/12. Therefore, B = tan^-1(5/12).

⚠️ COMMON MISTAKE: Students often get confused between the use of tan^-1 and cot^-1. However, since we are given the sides opposite and adjacent to angle B, we should use tan^-1 to find the angle B.