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Trigonometry Flashcards

7 cards from real TMUA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Trigonometry flashcards as text

  1. In a triangle with sides a = 5, b = 7, and included angle C = 60°, what is side c?

    Answer: √39

    By the cosine rule: c² = 25 + 49 - 2(5)(7)cos60° = 74 - 35 = 39, so c = √39.

  2. Which of the following is the correct expression for the area of a triangle with sides a, b and included angle C?

    Answer: (1/2)ab·sin(C)

    The area formula using two sides and the included angle is Area = (1/2)ab·sin(C).

  3. What is the value of arcsin(sin(5π/6))?

    Answer: π/6

    sin(5π/6) = 1/2, and arcsin returns values in [-π/2, π/2], so arcsin(1/2) = π/6.

  4. If tan(x) = -√3 and x ∈ [π/2, π], what is x?

    Answer: 2π/3

    tan(x) = -√3 and x is in Q2, so x = π - π/3 = 2π/3.

  5. Which identity correctly represents cos²(x) in terms of cos(2x)?

    Answer: (1 + cos(2x))/2

    From cos(2x) = 2cos²x - 1, rearranging gives cos²x = (1 + cos2x)/2.

  6. Given that sin(A) = 5/13 and cos(B) = 4/5, with A and B both in the first quadrant, find sin(A + B).

    Answer: 56/65

    cos A = 12/13, sin B = 3/5; sin(A+B) = sinAcosB + cosAsinB = (5/13)(4/5) + (12/13)(3/5) = 20/65 + 36/65 = 56/65.

  7. What is the number of solutions to sin(2x) = 0.5 in the interval [0, 2π]?

    Answer: 4

    Let u = 2x ∈ [0, 4π]; sin(u) = 0.5 has 4 solutions: π/6, 5π/6, π/6+2π, 5π/6+2π.