Cosine of the Angle between Vectors?

📌 CONCEPT: Inverse trigonometric functions, specifically the cosine function, can be used to find the angle between two vectors in a given triangle.

📐 RULE / FORMULA: The cosine of the angle between two vectors can be calculated using the dot product formula: cos(θ) = (a · b) / (|a| |b|), where θ is the angle between the vectors a and b.

💡 WORKED EXAMPLE: Given that cos(BAC) = 3/5, we can use this to find the value of cos(CDB). Since AB = AC = √2 and BC = 1, we can first find the angle BAC using the given cosine value. Then, we can use the fact that CDB is the angle between the vectors AB and BC to find the cosine of CDB using the dot product formula.

⚠️ COMMON MISTAKE: Students often forget to consider the magnitude of the vectors when using the dot product formula to find the cosine of the angle between them.