AMC12 Trigonometry 1 — Questions and Answers
Question 1: What is sin(30°)?
- 1/2 (Correct answer)
- √3/2
- 1
- √2/2
Correct answer: 1/2
sin(30°) = 1/2, a standard value from the 30-60-90 triangle.
Question 2: What is cos(π)?
- −1 (Correct answer)
- 0
- 1
- −1/2
Correct answer: −1
cos(π) = −1 since π radians corresponds to 180°.
Question 3: Simplify sin²(θ) + cos²(θ).
- 1 (Correct answer)
- 2
- 0
- sin(2θ)
Correct answer: 1
The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for all θ.
Question 4: What is the period of y = sin(2x)?
- π (Correct answer)
- 2π
- π/2
- 4π
Correct answer: π
The period of sin(bx) is 2π/b = 2π/2 = π.
Question 5: In a right triangle with hypotenuse 10 and one angle 30°, the side opposite that angle has length:
- 5 (Correct answer)
- 5√3
- 10/√3
- 2
Correct answer: 5
Opposite = hypotenuse × sin(30°) = 10 × 1/2 = 5.
Question 6: What is tan(45°)?
- 1 (Correct answer)
- √3
- 1/√3
- 0
Correct answer: 1
tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.
AMC12 Trigonometry 1
What is sin(30°)?