NBT NBT Mathematics: Trigonometry 1 — Questions and Answers
Question 1: If sin θ = 3/5 and θ is in the first quadrant, what is cos θ?
- 4/5 (Correct answer)
- 3/4
- 5/4
- 5/3
Correct answer: 4/5
Using the Pythagorean identity, cos θ = √(1 − sin²θ) = √(1 − 9/25) = √(16/25) = 4/5.
Question 2: What is the exact value of sin 30° × cos 60°?
- 1/4 (Correct answer)
- 1/2
- √3/4
- 3/4
Correct answer: 1/4
sin 30° = 1/2 and cos 60° = 1/2, so their product is 1/4.
Question 3: In which quadrant is θ if sin θ < 0 and cos θ > 0?
- Quadrant IV (Correct answer)
- Quadrant I
- Quadrant II
- Quadrant III
Correct answer: Quadrant IV
In Quadrant IV, sine is negative and cosine is positive, matching the given conditions.
Question 4: Simplify: sin²x + cos²x + tan²x − sec²x
- 0 (Correct answer)
- 1
- 2
- −1
Correct answer: 0
sin²x + cos²x = 1, and tan²x − sec²x = −1, so the full expression equals 1 + (−1) = 0.
Question 5: The period of y = sin(2x) is:
- π (Correct answer)
- 2π
- π/2
- 4π
Correct answer: π
The period of y = sin(bx) is 2π/b; with b = 2, the period is 2π/2 = π.
Question 6: Solve for θ ∈ [0°, 360°]: 2sin θ − 1 = 0
- θ = 30° or 150° (Correct answer)
- θ = 60° or 120°
- θ = 45° or 135°
- θ = 30° or 330°
Correct answer: θ = 30° or 150°
2sin θ = 1 gives sin θ = 1/2; the solutions in [0°, 360°] are θ = 30° and θ = 150°.
Question 7: In triangle ABC, angle B = 90°, AB = 5 and BC = 12. What is sin A?
- 12/13 (Correct answer)
- 5/13
- 12/5
- 5/12
Correct answer: 12/13
AC = √(5² + 12²) = 13 (hypotenuse); sin A = opposite/hypotenuse = BC/AC = 12/13.
NBT NBT Mathematics: Trigonometry 1
If sin θ = 3/5 and θ is in the first quadrant, what is cos θ?