Cosine Function in Triangles?

📌 CONCEPT: The cosine of an angle in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

📐 RULE / FORMULA: The cosine function is given by the formula: cos(θ) = adjacent side / hypotenuse.

💡 WORKED EXAMPLE: In a right-angled triangle, the length of the adjacent side to an angle is 12 units and the hypotenuse is 13 units. Using the cosine formula, we find cos(θ) = 12/13 = 0.9231. This value remains the same for all similar triangles because the ratio of the lengths of the sides remains constant.

⚠️ COMMON MISTAKE: Students may incorrectly assume that the cosine of an angle changes in different triangles, whereas it remains the same for all similar triangles as the ratio of the sides remains constant.