AMC12 Trigonometry & Precalculus 1 — Questions and Answers
Question 1: What is sin(30) + cos(60)?
- sqrt(3)
- sqrt(2)
- 1/2
- 1 (Correct answer)
Correct answer: 1
sin(30)=1/2 and cos(60)=1/2, so their sum is 1.
Question 2: In a right triangle, tan(theta)=3/4. What is sin(theta)?
- 4/5
- 3/4
- 4/3
- 3/5 (Correct answer)
Correct answer: 3/5
Opposite=3, adjacent=4, hypotenuse=5, so sin(theta)=3/5.
Question 3: What is the period of f(x) = sin(3x)?
- 3pi
- 2pi
- pi/3
- 2pi/3 (Correct answer)
Correct answer: 2pi/3
The period is 2pi/|b|=2pi/3.
Question 4: What is cos(135 degrees)?
- sqrt(2)/2
- sqrt(3)/2
- -sqrt(3)/2
- -sqrt(2)/2 (Correct answer)
Correct answer: -sqrt(2)/2
135 is in Q2 where cosine is negative; cos(135)=-cos(45)=-sqrt(2)/2.
Question 5: If sin(x)=0.6 with x in the first quadrant, what is tan(x)?
- 4/5
- 3/5
- 0.6
- 3/4 (Correct answer)
Correct answer: 3/4
cos(x)=sqrt(1-0.36)=0.8, so tan(x)=0.6/0.8=3/4.
Question 6: What is the amplitude of y = -3sin(2x)?
- -3
- 2
- 6
- 3 (Correct answer)
Correct answer: 3
The amplitude is the absolute value of the leading coefficient: |-3|=3.
AMC12 Trigonometry & Precalculus 1
What is sin(30) + cos(60)?