WAEC 2016 Mathematics · Question 8
If cos = x and sin 60o = x + 0.5 0o < < 90o, find, correct to the nearest degree, the value of
Options
- A.32o
- B.40o
- C.60o
- D.69o
Answer: D. 69o
Explanation written with AI and checked against the answer key
Analyze the question We are told cos θ = x and sin 60° = x + 0.5, with 0° < θ < 90°. We need θ to the nearest degree. Concept Use sin 60° = √3/2 ≈ 0.8660 to find x, then use x = cos θ and the inverse cosine to find θ. Solution Step 1: Find x. x + 0.5 = sin 60° = 0.8660 x = 0.8660 − 0.5 = 0.3660 Step 2: Find θ. cos θ = 0.3660 θ = cos⁻¹(0.3660) cos 68° ≈ 0.3746 and cos 69° ≈ 0.3584, so 0.3660 lies between them. The difference from cos 68° is 0.3746 − 0.3660 = 0.0086, and the gap between the two values is 0.0162. That gives about 0.53 of the way from 68° to 69°, so θ ≈ 68.5°. Checking more precisely: cos⁻¹(0.36603) ≈ 68.53°, which rounds to 69°. Answer Tip When the question says "correct to the nearest degree," compute the value to one decimal place first (68.53°) and then round. Also check the options by substitution: cos 60° = 0.5 and cos 40° = 0.77 are too large, so only a value near 69° gives about 0.366.AI can make mistakes. Report anything that looks wrong.
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