If sin θ = 3/5 (acute), find cos θ.

**The reasoning** You're given sin θ = 3/5, which means opposite/hypotenuse = 3/5 in a right triangle. Think of it as: opposite side = 3, hypotenuse = 5. To find cos θ (which is adjacent/hypotenuse), you need the adjacent side. Use **Pythagoras' theorem**: opposite² + adjacent² = hypotenuse² 3² + adjacent² = 5² 9 + adjacent² = 25 adjacent² = 16 adjacent = 4 Therefore, cos θ = adjacent/hypotenuse = **4/5** **Why the wrong options tempt you** - **A) 3/4**: You might mistakenly think cos θ = opposite/adjacent, forgetting that cosine needs the hypotenuse in the denominator. - **C) 5/4 and D) 4/3**: These flip the fraction or mix up which number goes where — impossible anyway since cos θ must be ≤ 1 for acute angles! **Quick takeaway** When you know sin θ = opposite/hypotenuse, always use Pythagoras to find the missing side, then cos θ = adjacent/hypotenuse. The hypotenuse (5) stays in the denominator for both!