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
What is the value of sin(π/6)?
Answer: 1/2
sin(π/6) = sin(30°) = 1/2 by the standard unit circle values.
What is the modulus of the complex number 3 + 4i?
Answer: 5
The modulus is √(3² + 4²) = √(9 + 16) = √25 = 5.
If z = 1 + i, what is z²?
Answer: 2i
(1 + i)² = 1 + 2i + i² = 1 + 2i − 1 = 2i.
Which expression equals cos(2θ)?
Answer: 2cos²(θ) − 1
The double-angle identity gives cos(2θ) = 2cos²(θ) − 1.
What is the argument (principal angle) of the complex number −1 + i?
Answer: 3π/4
Since −1 + i lies in the second quadrant, its argument is π − π/4 = 3π/4.
What is the value of sin²(θ) + cos²(θ) for all θ?
Answer: 1
The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for all real θ.
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