1. The document is a math exam with 20 multiple choice questions about trigonometric functions.
2. The questions cover topics like trigonometric ratios, trigonometric identities, solving trigonometric equations, and applying trigonometric functions to geometric problems involving angles and sides of triangles.
3. The correct answers to each question are provided as multiple choice options a, b, c, or d.
1. The document is a math exam with 20 multiple choice questions about trigonometric functions.
2. The questions cover topics like trigonometric ratios, trigonometric identities, solving trigonometric equations, and applying trigonometric functions to geometric problems involving angles and sides of triangles.
3. The correct answers to each question are provided as multiple choice options a, b, c, or d.
1. The document is a math exam with 20 multiple choice questions about trigonometric functions.
2. The questions cover topics like trigonometric ratios, trigonometric identities, solving trigonometric equations, and applying trigonometric functions to geometric problems involving angles and sides of triangles.
3. The correct answers to each question are provided as multiple choice options a, b, c, or d.
1. The document is a math exam with 20 multiple choice questions about trigonometric functions.
2. The questions cover topics like trigonometric ratios, trigonometric identities, solving trigonometric equations, and applying trigonometric functions to geometric problems involving angles and sides of triangles.
3. The correct answers to each question are provided as multiple choice options a, b, c, or d.
𝜋 1. , then sin 𝛽 is equal to 2 13 63 61 3 5 a) 65 b) 65 c) 5 d) 13 𝜋 3𝜋 5𝜋 7𝜋 2. The value of sin sin sin sin , is 14 14 14 14 a) 1 b) 1/4 c) 1/8 d) 2/7 3. If 𝜃1,𝜃2,𝜃3,𝜃4 are roots of the equation sin(𝜃 + 𝛼) = 𝑘sin 2 𝜃 no two of which differ by a multiple of 2 𝜋, then 𝜃1 + 𝜃2 + 𝜃3 + 𝜃4 is equal to a) 2𝑛 𝜋, 𝑛 ∈ 𝑍 b) (2𝑛 + 1)𝜋, 𝑛 ∈ 𝑍 c) 𝑛 𝜋,𝑛 ∈ 𝑍 d)None of these 3𝜋 4. The radius of the circle whose arc of length 15𝜋 cm makes an angle of 4 radian at the centre is 1 1 a) 10 cm b) 20 cm c) 114 cm d)222 cm 5. The value of cot 𝜃 ― tan 𝜃 ―2tan 2𝜃 ―4tan 4𝜃 ―8cot 8𝜃, is a) 0 b) 1 c) ―1 d)None of these 6. In a triangle 𝐴𝐵𝐶,𝑏 = 3,𝑐 = 1 and ∠𝐴 = 30°, then the measure of the largest angle of the triangle is a) 60° b) 135° c) 90° d)120° 7. The maximum value of 3cos 𝜃 + 4 sin 𝜃 is a) 3 b) 4 c) 5 d)None of these 8. If the sides of a triangle are proportional to 2, and 6 3 ―1, the greatest and the least angles of the triangle are a) 120°,15° b) 90°,15° c) 75°,45° d)150°,15° 9. In a ∆𝐴𝐵𝐶 if 𝑟1 = 16,𝑟2 = 48 𝑎𝑛𝑑 𝑟3 = 24, then its in-radius is a) 7 b) 8 c) 6 d)None of these 10. The number of values of 𝑥 in the interval [0, 5𝜋] satisfying the equation 3 sin2 𝑥 ― 7 sin 𝑥 + 2 = 0 is a) 0 b) 5 c) 6 d)10 2 11. If cos θ = cos 2θ, then the general value of θ is 𝑛π 𝑛π a) 𝑛π b) 2𝑛π c) 3 d) 2 sin 2 𝑥+2 cos2 𝑥 1―sin 2 𝑥+2 sin2 𝑥 12. The equation 3 +3 = 28 is satisfied for the values of 𝑥 given by a) cos 𝑥 = 0,tan 𝑥 = ―1 b) tan 𝑥 = ―1,cos 𝑥 = 1 c) tan 𝑥 = 1, cos 𝑥 = 0 d)None of these 13. The minimum value of 27cos 2𝑥 81sin 2𝑥 is 1 1 1 a) ―5 b) 5 c) 243 d) 27 14. Let 0 < 𝑥 ≤ 𝜋/4, then (sec 2𝑥 ― tan 2𝑥) equals a) tan2(𝑥 + 𝜋/4) b) tan(𝑥 + 𝜋/4) c) tan(𝜋/4 ― 𝑥) d)tan(𝑥 ― 𝜋/4) 1 1 15. The number of solutions of the equation sin5 𝑥 ― cos5 𝑥 = ― ( sin 𝑥 ≠ cos 𝑥) is cos 𝑥 sin 𝑥 a) 0 b) 1 c) Infinite d)None of these 4 5 𝜋 16. Let cos(𝛼 + 𝛽) = and let sin(𝛼 ― 𝛽) = , where 0 ≤ 𝛼, 𝛽 ≤ 4. Then tan 2𝛼 is equal to 5 13 25 56 19 20 a) 16 b) 33 c) 12 d) 7 2𝜋 4𝜋 6𝜋 17. The value of cos + cos + cos , is 7 7 7 a) 1 b) ―1 c) 1/2 d) ―1/2 18. If in a triangle 𝑎cos (2) +𝑐cos (2) = 2 𝐶 2 𝐴 3𝑏 2 , then the sides of the triangle are in a) AP b) GP c) HP d)None of these 1 ― cos 2θ 19. If 1 + cos 2θ = 3, then the general value of θ is 𝜋 𝜋 𝜋 𝜋 a) 2𝑛𝜋 ± 6 b) 𝑛𝜋 ± 6 c) 2𝑛𝜋 ± 3 d)𝑛𝜋 ± 3 31 20. In a ∆𝐴𝐵𝐶, if 𝑎 = 5 cm,𝑏 = 4 cm and cos(𝐴 ― 𝐵) = , then cos 𝐶 = 32 a) 1/4 b) 1/8 c) 1/6 d)1/2