Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Trigonometry Flashcards

6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. What does sin(A + B) equal?

    Answer: sinA cosB + cosA sinB

    The sine angle addition formula is sin(A+B) = sinA cosB + cosA sinB.

  2. If sin(θ) = 3/5 and θ is in quadrant I, what is cos(θ)?

    Answer: 4/5

    By the Pythagorean identity, cos(θ) = √(1 − 9/25) = √(16/25) = 4/5.

  3. What is sin(2θ) if sin(θ) = 1/2 and θ is in the first quadrant?

    Answer: √3/2

    sin(2θ) = 2sin(θ)cos(θ) = 2 × (1/2) × (√3/2) = √3/2.

  4. In a triangle with sides a = 7, b = 8 and included angle C = 60°, side c equals:

    Answer: √57

    By the law of cosines: c² = 49 + 64 − 2(7)(8)cos(60°) = 113 − 56 = 57, so c = √57.

  5. What is the exact value of cos(75°)?

    Answer: (√6 − √2)/4

    cos(75°) = cos(45°+30°) = (√2/2)(√3/2) − (√2/2)(1/2) = (√6−√2)/4.

  6. For 2sin(x) = √2 on [0, 2π], how many solutions are there?

    Answer: 2

    sin(x) = √2/2 gives x = π/4 and x = 3π/4, exactly 2 solutions in [0, 2π].