/20 1234567891011121314151617181920 Test Code: MC8L2 1 / 20 1. If 3 cot A = 4, find sec A. A) 5/3 B) 5/4 C) 3/5 D) 4/5 cot A = 4/3 ⇒ base = 4k, height = 3k ⇒ hypotenuse = 5k ⇒ sec A = hyp/base = 5/4. 2 / 20 2. If cot θ = 8/7, then what is sin θ? A) 8/13 B) 7/13 C) 13/8 D) 13/7 Let base = 8k, perpendicular = 7k hypotenuse = √(64k² + 49k²) = √113k ⇒ sin θ = 7/√113 ⇒ rationalized. 3 / 20 3. Evaluate: 9 sec² A – 9 tan² A = ? A) 9 B) 1 C) 0 D) -1 sec² A – tan² A = 1 ⇒ Multiply by 9 ⇒ 9(sec² A – tan² A) = 9 4 / 20 4. Value of cos²38° cos²52° – sin²38° sin²52° is: A) 1 B) 0 C) -1 D) Undefined cos A cos B – sin A sin B = cos(A + B) ⇒ cos 90° = 0 5 / 20 5. If sec 4A = cosec (A – 20°), then A = ? A) 20° B) 30° C) 22° D) 18° sec 4A = cosec(A–20°) cosec(90–4A) = cosec(A–20°) 90–4A = A–20 ⇒ A = 22° 6 / 20 6. Evaluate (sec A + tan A)(1 – sin A) = ? A) 1 B) sin A C) 0 D) cos A 7 / 20 7. If cot A = x, then sin A = ? A) x/√(x²+1) B) None C) 1/√(x²+1) D) √(x²+1)/x Let cot A = x = base/perp ⇒ hyp² = x² + 1 ⇒ sin A = 1/√(x² + 1) 8 / 20 8. If tan A = cot B, then A + B = ? A) 90° B) 60° C) 45° D) 180° tan A = cot B tan A = tan(90–B) A = 90–B ⇒ A + B = 90° 9 / 20 9. Evaluate sin60° cos30° + sin30° cos60° A) 0.5 B) 1 C) √3/2 D) 0 Explanation: = (√3/2)(√3/2) + (1/2)(1/2) = 3/4 + 1/4 = 1 10 / 20 10. If tan 2A = cot (A − 18°), then A = ? A) 30° B) 18° C) 45° D) 36° tan 2A = cot(A−18°) cot(90−2A) = cot(A−18°) 90–2A = A–18 3A = 108 ⇒ A = 36° 11 / 20 11. If 15 cot A = 8, what is sin A? A) 8/13 B) 8/15 C) 8/17 D) 5/13 cot A = 8/15 ⇒ base = 8k, perpendicular = 15k ⇒ hyp = √(64k² + 225k²) = √289k² = 17k ⇒ sin A = 15/17 12 / 20 12. If A + B = 60° and A – B = 30°, then A = ? A) 45° B) 35° C) 30 D) 40° Add: 2A = 90 ⇒ A = 45° 13 / 20 13. In triangle PQR with right angle at Q, PQ = 5 cm and PR + QR = 25 cm. Find tan P. A) 13/5 B) 5/13 C) 12/5 D) 5/12 Let PR = x, so QR = 25 – x. Use Pythagoras: x² = 5² + (25–x)² ⇒ Solve⇒ x = 13, QR = 12 ⇒ tan P = QR/PQ = 12/5 14 / 20 14. Is tan A always < 1? A) True B) False C) Undefined D) Sometimes Example: triangle with sides 5, 12, 13 ⇒ tan A = 12/5 = 2.4 > 1 ⇒ false. 15 / 20 15. If sin A = cos A, then A = ? A) 30° B) 0° C) 60° D) 45° sin A = cos A ⇒ tan A = 1 ⇒ A = 45° 16 / 20 16. In ΔABC, right-angled at B, if AB = 24 cm, BC = 7 cm, what is sin A and cos A? A) sin A = 24/25, cos A = 25/24 B) sin A = 7/25, cos A = 24/25 C) sin A = 7/24, cos A = 24/25 D) sin A = 24/25, cos A = 7/25 By Pythagoras: AC² = AB² + BC² = 576 + 49 = 625 ⇒ AC = 25 ⇒ sin A = BC/AC = 7/25, cos A = AB/AC = 24/25 17 / 20 17. Value of sin² 25° + cos² 25° = ? A) Cos 60° B) 1 C) 0 D) sin 50° By identity: sin² θ + cos² θ = 1 18 / 20 18. If sec θ = 13/12, what is sin θ? A) 12/5 B) 5/13 C) 13/12 D) 12/13 sec θ = hyp/adj = 13k/12k ⇒ height² = hyp² – base² = 169 – 144 = 25 ⇒ sin θ = 5/13 19 / 20 19. If sin A = 3/5, find cos A. A) 4/5 B) 3/4 C) 5/3 D) 4/3 Let triangle with sides 3k (opposite), 5k (hypotenuse) ⇒ base² = 25k² – 9k² = 16k² base = 4k ⇒ cos A = base/hyp = 4/5 20 / 20 20. If sin A = 3/5 and cos C = 3/5 in right triangle, what is sin A cos C + cos A sin C? A) 9/25 B) 1 C) 25/24 D) 24/25 cos A = 4/5, sin C = 4/5 ⇒ sin A cos C + cos A sin C = (3×3 + 4×4)/25 = 25/25 = 1 Send feedback
