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

What is sin(30°) + cos(60°)?
Answer: 1
sin(30°)=1/2 and cos(60°)=1/2; sum=1.
If cos(θ) = 3/5 and θ is in the first quadrant, find sin(θ).
Answer: 4/5
sin^2(θ)+cos^2(θ)=1 gives sin^2(θ)=1-9/25=16/25, so sin(θ)=4/5.
What is the value of tan(45°)?
Answer: 1
tan(45°)=sin(45°)/cos(45°)=(√2/2)/(√2/2)=1.
Find the modulus of the complex number z = 3 + 4i.
Answer: 5
|z|=√(3^2+4^2)=√(9+16)=√25=5.
Compute (2+3i)(1-i).
Answer: 5+i
(2+3i)(1-i)=2-2i+3i-3i^2=2+i+3=5+i.
What is i^10 (where i = √(-1))?
Answer: -1
i^10=(i^4)^2·i^2=1·(-1)=-1.