NBT NBT Mathematics: Trigonometry 3 — Questions and Answers
Question 1: Express cos(180° − θ) in terms of cos θ.
- −cos θ (Correct answer)
- cos θ
- sin θ
- −sin θ
Correct answer: −cos θ
Using the co-function reduction formula, cos(180° − θ) = −cos θ.
Question 2: The graph of y = cos x has a maximum value at x equal to:
- 0° (Correct answer)
- 90°
- 180°
- 270°
Correct answer: 0°
y = cos x reaches its maximum value of 1 at x = 0° (and x = 360°, etc.).
Question 3: Given sin 40° ≈ 0.643, what is cos 50°?
- 0.643 (Correct answer)
- 0.766
- 0.357
- 0.500
Correct answer: 0.643
Since 40° and 50° are complementary angles, cos 50° = sin 40° ≈ 0.643.
Question 4: Solve cos θ = −1 for θ ∈ [0°, 360°].
- 180° (Correct answer)
- 0° and 360°
- 90° and 270°
- No solution
Correct answer: 180°
cos θ = −1 only at θ = 180° within [0°, 360°].
Question 5: What is the value of 2sin 60° − cos 30°?
- √3/2 (Correct answer)
- √3
- 3√3/2
- 0
Correct answer: √3/2
2sin 60° = 2 × (√3/2) = √3 and cos 30° = √3/2, so √3 − √3/2 = √3/2.
Question 6: The graph of y = sin x is shifted 30° to the right. Its equation becomes:
- y = sin(x − 30°) (Correct answer)
- y = sin(x + 30°)
- y = sin x − 30
- y = sin x + 30
Correct answer: y = sin(x − 30°)
A horizontal shift of 30° to the right replaces x with (x − 30°), giving y = sin(x − 30°).
Question 7: Using the Sine Rule, in triangle ABC if a = 10, sin A = 0.5, and sin B = 0.8, find b.
- 16 (Correct answer)
- 6.25
- 4
- 8
Correct answer: 16
By the Sine Rule: b/sin B = a/sin A → b = 10 × 0.8/0.5 = 16.
NBT NBT Mathematics: Trigonometry 3
Express cos(180° − θ) in terms of cos θ.