NBT NBT Mathematics: Trigonometry 2 — Questions and Answers
Question 1: What is the value of tan 45°?
- 1 (Correct answer)
- √2
- 1/√2
- 0
Correct answer: 1
At 45°, sin 45° = cos 45° = 1/√2, so tan 45° = sin/cos = 1.
Question 2: The amplitude of y = 3sin(x) is:
- 3 (Correct answer)
- 1
- 2π
- π
Correct answer: 3
The amplitude of y = A sin(x) is |A|; here A = 3, so the amplitude is 3.
Question 3: If cos θ = −√3/2 and 180° < θ < 270°, what is θ?
- 210° (Correct answer)
- 150°
- 240°
- 330°
Correct answer: 210°
cos 30° = √3/2, so the reference angle is 30°; in Quadrant III, θ = 180° + 30° = 210°.
Question 4: Which identity is correct?
- 1 + cot²θ = cosec²θ (Correct answer)
- 1 + tan²θ = cos²θ
- sin²θ − cos²θ = 1
- cosec²θ = tan²θ + 1
Correct answer: 1 + cot²θ = cosec²θ
The identity 1 + cot²θ = cosec²θ is derived from dividing sin²θ + cos²θ = 1 by sin²θ.
Question 5: On the unit circle, the point (0, −1) corresponds to which angle?
- 270° (Correct answer)
- 90°
- 180°
- 360°
Correct answer: 270°
The point (0, −1) on the unit circle corresponds to 270° (or 3π/2 radians).
Question 6: What is the general solution of sin θ = 0?
- θ = n × 180°, n ∈ ℤ (Correct answer)
- θ = 90° + n × 180°, n ∈ ℤ
- θ = n × 360°, n ∈ ℤ
- θ = 45° + n × 90°, n ∈ ℤ
Correct answer: θ = n × 180°, n ∈ ℤ
sin θ = 0 at every multiple of 180° (i.e., 0°, 180°, 360°, …), so θ = n × 180°.
Question 7: In triangle PQR, PQ = 7 cm, QR = 24 cm, and angle Q = 90°. Find tan P.
- 24/7 (Correct answer)
- 7/24
- 7/25
- 24/25
Correct answer: 24/7
tan P = opposite/adjacent = QR/PQ = 24/7.
NBT NBT Mathematics: Trigonometry 2
What is the value of tan 45°?