Trigonometry & Precalculus Flashcards
6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning โ missed cards come back until you master them.
Read the first 6 Trigonometry & Precalculus flashcards as text
What is tan(45) + tan(225)?
Answer: 2
tan has period 180, so tan(225)=tan(45)=1; sum=1+1=2.
Which expression equals sin^2(x) + cos^2(x)?
Answer: 1
This is the fundamental Pythagorean identity: sin^2(x)+cos^2(x)=1 for all x.
What is the maximum value of y = 2cos(x) - 1?
Answer: 1
cos(x) achieves maximum 1, giving y_max=2(1)-1=1.
In a triangle with a=7, b=8, and angle C=60, what is the area?
Answer: 14sqrt(3)
Area=(1/2)*a*b*sin(C)=(1/2)(7)(8)(sqrt(3)/2)=14sqrt(3).
What is sin(pi/4) * cos(pi/4)?
Answer: 1/2
(sqrt(2)/2)*(sqrt(2)/2)=2/4=1/2.
What is the range of y = arcsin(x)?
Answer: [-pi/2,pi/2]
The principal value range of arcsin is [-pi/2,pi/2] by definition.