AMC 12 Trigonometry & Complex Numbers Flashcards
6 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 AMC 12 Trigonometry & Complex Numbers flashcards as text
Using the Law of Cosines with a = 5, b = 7, and C = 60°, what is c²?
Answer: 39
c² = 5² + 7² − 2(5)(7)cos(60°) = 25 + 49 − 35 = 39.
What is the principal argument of the complex number i?
Answer: π/2
The number i has real part 0 and imaginary part 1, placing it at angle π/2 on the unit circle.
What is the period of f(x) = sin(2x)?
Answer: π
The period of sin(bx) is 2π/b; with b = 2 the period is 2π/2 = π.
De Moivre's theorem states that (r·e^(iθ))^n equals which of the following?
Answer: r^n · e^(inθ)
De Moivre's theorem: (r(cosθ + i sinθ))^n = r^n(cos(nθ) + i sin(nθ)).
If cos(θ) = 3/5 and θ is in the first quadrant, what is sin(θ)?
Answer: 4/5
sin²θ = 1 − (3/5)² = 1 − 9/25 = 16/25, so sinθ = 4/5.
What is the imaginary part of z = 4e^(iπ/3)?
Answer: 2√3
4e^(iπ/3) = 4(cos(π/3) + i sin(π/3)) = 4·(1/2) + 4·(√3/2)·i, giving imaginary part 2√3.
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