68 free MCQs on Trigonometric Functions, each with its own worked answer and explanation. Ratios, identities, and applications in triangles
Take the timed Trigonometric Functions chapterwise test →68 practice questions on Trigonometric Functions, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Trigonometric Functions notes.
Unit circle with standard angles 0, 30, 45, 60, 90 degrees; at 45 degrees the point is (cos45, sin45) = (1/sqrt2, 1/sqrt2).
Q4.
The fundamental trigonometric identity is:
Q9.
In a right triangle with hypotenuse 5 and opposite 3, sin θ =
Q13.
If sin A = 5/13, find cos A (in a right triangle).
Q22.
Prove that (1+tanθ)² + (1+cotθ)² = (secθ + cosecθ)². LHS equals:
Q23.
sin(A+B) when A = 30°, B = 60°:
Q27.
cos(A-B) - cos(A+B) =
Q30.
Express sin 3A in terms of sin A.
Q31.
In triangle ABC, if A = 60°, b = 3, c = 4, find a (cosine rule).
Q32.
Height of a tower from a point 50m away at elevation 30° is:
Q33.
Find the general solution of sin θ = 1/2.
Q34.
cos 2A = 1 - 2sin²A. Verify for A = 30°:
Q37.
If sin A = 3/5 and A is in second quadrant, cos A =
Q38.
The range of sin x for all x is:
Q40.
In a triangle, if a = 5, b = 6, c = 7, use the cosine rule to find angle A:
Q41.
Solve: 2cos²θ - 3cosθ + 1 = 0. Find all solutions in [0, 2π].
Q42.
In a triangle, prove R = a/(2sinA). If a = 8, A = 30°, find R.
Q43.
If tan α = 1/7 and sin β = 1/√10, find value of α + 2β (in first quadrant).
Q44.
General solution of 2cos²x + 3sinx = 0 is:
Q45.
tan(A+B+C) formula: if A+B+C = π, then tanA + tanB + tanC =
Q47.
In triangle ABC, if b + c = 2a, then tanB/2 × tanC/2 =
Q48.
Sum of cosines: cosθ + cos(θ+2π/n) + cos(θ+4π/n) + ... (n terms) =
Q49.
If sin θ = 3/5 and θ is in second quadrant, find tan 2θ.
Q51.
In triangle ABC, a/(sinA) = 2R. This is the:
Q53.
If in triangle ABC, a = 3, b = 4, C = 90°, find area using trigonometry.
Q54.
Solve tan²θ - 3 = 0 for θ in (0, 2π).
Q57.
In triangle, sin(A/2) = √[(s-b)(s-c)/bc]. This is:
Q58.
If tan(x+y) = 33 and tan(x) = 3, find tan(y).
Q60.
The exact value of sin 75° is:
Q63.
The number of solutions of tanx + secx = 2cosx in [0, 2π) is:
Q64.
In a triangle ABC, tanA + tanB + tanC = 6 and tanA·tanB = 2. Then tanC equals:
Q65.
The range of f(x) = 3sinx + 4cosx + 5 is:
Q66.
If tanθ = 3/4 and θ lies in the third quadrant, then sinθ + cosθ equals:
Q67.
The value of sin²(π/8) + sin²(3π/8) + sin²(5π/8) + sin²(7π/8) is:
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