If sin θ = 3/5, find cos θ (acute angle).

**The reasoning** You're given sin θ = 3/5. Think of this as a right triangle where the **opposite side = 3** and the **hypotenuse = 5**. To find cos θ, you need the adjacent side. Use **Pythagoras' theorem**: hyp² = opp² + adj² 5² = 3² + adj² 25 = 9 + adj² adj² = 16 adj = 4 So cos θ = adjacent/hypotenuse = **4/5** ✓ **Why the wrong options tempt you** - **A) 3/4** — You might flip the fraction wrongly or divide opposite by adjacent (that's actually tan θ!) - **C) 5/4** — Putting hypotenuse in the numerator breaks the rule; cosine can never be greater than 1 - **D) 4/3** — Again, this is greater than 1, which is impossible for any trig ratio involving the hypotenuse as denominator **Quick takeaway** Draw the triangle! SOH-CAH-TOA means cos θ is always **Adjacent/Hypotenuse**, and when you know sin, Pythagoras gives you the missing side. Your cosine answer must always be ≤ 1 for acute angles.