AMC12 Trigonometry & Precalculus 2 — Questions and Answers
Question 1: What is tan(45) + tan(225)?
- 0
- 1
- -1
- 2 (Correct answer)
Correct answer: 2
tan has period 180, so tan(225)=tan(45)=1; sum=1+1=2.
Question 2: Which expression equals sin^2(x) + cos^2(x)?
- sin(2x)
- 0
- 2
- 1 (Correct answer)
Correct answer: 1
This is the fundamental Pythagorean identity: sin^2(x)+cos^2(x)=1 for all x.
Question 3: What is the maximum value of y = 2cos(x) - 1?
- 2
- -1
- 3
- 1 (Correct answer)
Correct answer: 1
cos(x) achieves maximum 1, giving y_max=2(1)-1=1.
Question 4: In a triangle with a=7, b=8, and angle C=60, what is the area?
- 28sqrt(3)
- 7sqrt(3)
- 28
- 14sqrt(3) (Correct answer)
Correct answer: 14sqrt(3)
Area=(1/2)*a*b*sin(C)=(1/2)(7)(8)(sqrt(3)/2)=14sqrt(3).
Question 5: What is sin(pi/4) * cos(pi/4)?
- sqrt(2)/2
- 1/4
- sqrt(2)/4
- 1/2 (Correct answer)
Correct answer: 1/2
(sqrt(2)/2)*(sqrt(2)/2)=2/4=1/2.
Question 6: What is the range of y = arcsin(x)?
- [0,pi]
- (-pi,pi)
- [-1,1]
- [-pi/2,pi/2] (Correct answer)
Correct answer: [-pi/2,pi/2]
The principal value range of arcsin is [-pi/2,pi/2] by definition.
AMC12 Trigonometry & Precalculus 2
What is tan(45) + tan(225)?