Trigonometry and Complex Numbers Flashcards

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

Read the first 6 Trigonometry and Complex Numbers flashcards as text

In a right triangle, if sin(A) = 5/13, what is cos(A)?
Answer: 12/13
cos(A)=√(1-25/169)=√(144/169)=12/13.
What is the period of f(x) = sin(3x)?
Answer: 2π/3
The period of sin(kx) is 2π/k; for k=3, period=2π/3.
Compute the conjugate of z = 7 - 2i.
Answer: 7 + 2i
The complex conjugate of a+bi is a-bi; for 7-2i the conjugate is 7+2i.
Simplify (2+i)/(1-i).
Answer: (1+3i)/2
Multiply by (1+i)/(1+i): (2+i)(1+i)/((1-i)(1+i))=(2+3i+i^2)/2=(1+3i)/2.
Find all x in [0°, 360°) satisfying 2sin(x) = √2.
Answer: 45° and 135°
sin(x)=√2/2, so x=45° and x=135° in [0°,360°).
If z = 1 + i, what is z^2?
Answer: 2i
(1+i)^2=1+2i+i^2=1+2i-1=2i.