NBT NBT Mathematics: Trigonometry 4 — Questions and Answers
Question 1: What is tan(360° − θ) equivalent to?
- −tan θ (Correct answer)
- tan θ
- cot θ
- −cot θ
Correct answer: −tan θ
Using the reduction formula tan(360° − θ) = −tan θ (Quadrant IV, tangent is negative).
Question 2: If tan θ = −1 and θ ∈ (90°, 180°), find θ.
- 135° (Correct answer)
- 45°
- 225°
- 315°
Correct answer: 135°
The reference angle for tan = 1 is 45°; in Quadrant II, θ = 180° − 45° = 135°.
Question 3: Which of the following equals sin(90° + θ)?
- cos θ (Correct answer)
- −cos θ
- sin θ
- −sin θ
Correct answer: cos θ
Using the reduction formula, sin(90° + θ) = cos θ.
Question 4: The Cosine Rule states: a² = b² + c² − 2bc cos A. If b = 5, c = 7, A = 60°, find a².
- 39 (Correct answer)
- 74
- 4
- 109
Correct answer: 39
a² = 25 + 49 − 2(5)(7)(0.5) = 74 − 35 = 39.
Question 5: Which function has a range of (−∞, −1] ∪ [1, ∞)?
- y = sec x (Correct answer)
- y = sin x
- y = cos x
- y = tan x
Correct answer: y = sec x
The secant function sec x = 1/cos x has range y ≤ −1 or y ≥ 1, i.e., (−∞, −1] ∪ [1, ∞).
Question 6: Prove: (sin θ + cos θ)² = 1 + 2sin θ cos θ. The missing step uses:
- sin²θ + cos²θ = 1 (Correct answer)
- tan²θ + 1 = sec²θ
- cos(2θ) = 1 − 2sin²θ
- sin(2θ) = 2sin θ cos θ
Correct answer: sin²θ + cos²θ = 1
Expanding gives sin²θ + 2sin θ cos θ + cos²θ; replacing sin²θ + cos²θ with 1 gives 1 + 2sin θ cos θ.
Question 7: The area of triangle ABC with sides a = 8, b = 6, and included angle C = 30° is:
- 12 (Correct answer)
- 24
- 6√3
- 48
Correct answer: 12
Area = ½ab sin C = ½ × 8 × 6 × sin 30° = 24 × 0.5 = 12.
NBT NBT Mathematics: Trigonometry 4
What is tan(360° − θ) equivalent to?