Trigonometry Objective MCQs with Answers

Trigonometry Objective MCQs with Answers

For: LT Grade, TGT, PGT, CET, A.P. EAMCET, Karnataka CET and other exams.

Q25. The acute angle in radians between the minute and hour hands of a clock when the time is 4 hours 20 minutes is:
(a) π/18  (b) π/6  (c) π/12  (d) π/9
Answer: (c)

Q26. The general solution of the equation sinθ + cosθ = 1 is:
(a) nπ + (−1)ⁿπ/4  (b) 2nπ ± π/2  (c) 2nπ ± π/4  (d) 2nπ ± π/2
Answer: (d)

Q27. cos76° + cos²16° = cos76° cos16°
(a) 1/2  (b) 1  (c) –1  (d) 0
Answer: (d)

Q28. k = 2 cos²((2k – 1)π/12)
(a) 0  (b) 1  (c) 2  (d) 3
Answer: (d)

Q29. If (3 + 2i sinθ)/(1 – 2i sinθ) is a real number and 0 < θ < 2π, then:
(a) π  (b) π/2  (c) π/3  (d) π/4
Answer: (c)

Q30. If sin⁻¹x – cos⁻¹x = π/6, then x =
(a) √3/2  (b) 1/2  (c) 1 – √3  (d) –√3
Answer: (a)

Q31. sinh(ix) =
(a) i sinx  (b) sin(ix)  (c) i sin(ix)  (d) i sin x
Answer: (c)

Q32. The perimeter of a triangle is 16 cm. One side is 6 cm. If area is 12√3 cm², the triangle is:
(a) Right-angled  (b) Isosceles  (c) Equilateral  (d) Scalene
Answer: (c)

Q33. If the altitudes of a triangle are in arithmetic progression, then the sides are in:
(a) Arithmetic  (b) Harmonic  (c) Geometric  (d) Arithmetic-Geometric
Answer: (a)

Q34. If triangle ABC is right-angled at A, then r₁ + r₂ + r₃ =
(a) r₁ − r₂  (b) r₁ + r₂  (c) R  (d) r₁ + r₂ + r₃
Answer: (a)

Q35. If f(x) = sin²(x + π/8) + sin²(x − π/8), then period of f(x) is:
(a) π  (b) π/2  (c) 2π  (d) 4π
Answer: (c)

Q36. If cos(α + β) = 4/5, sin(α − β) = 5/13 and α, β ∈ (0, π/4), then 2α =
(a) 30°  (b) 33°  (c) 35°  (d) 36°
Answer: (a)

Q37. In triangle ABC, if a = 2x, b = 2y, ∠C = 120°, then area of triangle is:
(a) xy  (b) x√3y  (c) 2xy  (d) √3xy
Answer: (b)

Q38. sin⁶θ + cos⁶θ + 3 sin²θ cos²θ is equal to:
(a) 0  (b) 1  (c) –1  (d) none of these
Answer: (c)

Q39. If tan((B − C)/2) = x cot(A/2), then x =
(a) (a − b)/(c + a)  (b) (a − b)/(c − a)  (c) (b − c)/(b + c)  (d) none of these
Answer: (d)

Q40. If √3 cosθ + sinθ = √2, then general value of θ is:
(a) nπ + (–1)ⁿπ/4  (b) (–1)ⁿπ/4  (c) nπ ± π/3  (d) nπ ± π/4
Answer: (d)

Q41. If α + β = π/2 and β + γ = α, then tan α equals:
(a) 2(tan β + tan γ)  (b) tan β + tan γ  (c) tan β tan γ  (d) 2 tan β + 2 tan γ
Answer: (c)

Q42. If sin⁻¹(x − x³/2 + x⁵/4 − x⁷/6…) = π/2 for 0 < |x| < √2, then x equals:
(a) 1  (b) √2  (c) 1/√2  (d) 1/2
Answer: (b)

Tags: Trigonometry MCQs, Objective Questions, Maths Competitive Exams, LT Grade, TGT, PGT, CET, EAMCET