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GRE Trigonometric Functions — practice questions — page 2

Explore 45 free Trigonometric Functions questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometric Functions questions and exercises with answers

Showing questions 31–45 of 45.

The minute hand of a watch is 1.5 cm long. The distance the tip moves in 40 minutes is (use π = 3.14):Read the answer and worked solution →The radius of a circle where a central angle of 60° intercepts an arc of length 37.4 cm (use π = 22/7) is:Read the answer and worked solution →If two arcs of equal length subtend angles of 65° and 110° at the centres of two circles, the ratio of the radii r₁ : r₂ is:Read the answer and worked solution →If cos x = -3/5 and x lies in the THIRD quadrant, then sin x equals:Read the answer and worked solution →If cot x = -5/12 and x lies in the SECOND quadrant, then sin x equals:Read the answer and worked solution →In which quadrant is tan x POSITIVE while sin x is NEGATIVE?Read the answer and worked solution →The DOMAIN of y = tan x is:Read the answer and worked solution →sin(2nπ + x) equals (for any integer n):Read the answer and worked solution →The RANGE of y = sec x is:Read the answer and worked solution →At which of the following x-values is cos x equal to zero?Read the answer and worked solution →The value of cos(-π/3) is:Read the answer and worked solution →6 radians converts to approximately:Read the answer and worked solution →An angle of $90^\circ$ in radians is:Read the answer and worked solution →The value of $\sin(\pi/4)$ is:Read the answer and worked solution →The identity $\sin 2A$ equals:Read the answer and worked solution →

Worked practice questions

The minute hand of a watch is 1.5 cm long. The distance the tip moves in 40 minutes is (use π = 3.14):

  1. 9.42 cm
  2. 3.14 cm
  3. 6.28 cm
  4. 1.57 cm
Show answer and solution

Correct answer: C. 6.28 cm

40 minutes = 2/3 of a revolution → θ = (2/3) × 2π = 4π/3 radians. Distance l = rθ = 1.5 × (4π/3) = 2π cm = 2 × 3.14 = 6.28 cm.

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The radius of a circle where a central angle of 60° intercepts an arc of length 37.4 cm (use π = 22/7) is:

  1. 35.7 cm
  2. 17.85 cm
  3. 71.4 cm
  4. 11.9 cm
Show answer and solution

Correct answer: A. 35.7 cm

60° = π/3 radians. We have r = l/θ. That is r = 37.4/(π/3). That is r = 37.4 × 3/π. That is r = 37.4 × 3 × 7/22. So r = 35.7 cm.

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If two arcs of equal length subtend angles of 65° and 110° at the centres of two circles, the ratio of the radii r₁ : r₂ is:

  1. 22 : 13
  2. 110 : 65
  3. 65 : 110
  4. 13 : 22
Show answer and solution

Correct answer: A. 22 : 13

For equal arcs, l = r₁θ₁ = r₂θ₂ → r₁/r₂ = θ₂/θ₁ = 110/65 = 22/13. So r₁ : r₂ = 22 : 13. (The larger angle requires a smaller radius for equal arc length.)

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann Sums