NBT NBT Mathematics: Trigonometry 5 — Questions and Answers
Question 1: What is the range of y = sin x?
- [−1, 1] (Correct answer)
- (−∞, ∞)
- [0, 1]
- [−π, π]
Correct answer: [−1, 1]
The sine function oscillates between −1 and 1 inclusive, so its range is [−1, 1].
Question 2: Simplify: cos²θ − sin²θ
- cos(2θ) (Correct answer)
- 1
- 2cos²θ
- sin(2θ)
Correct answer: cos(2θ)
The double angle identity states cos(2θ) = cos²θ − sin²θ.
Question 3: If tan θ = 5/12 and θ is acute, find sin θ.
- 5/13 (Correct answer)
- 12/13
- 5/12
- 12/5
Correct answer: 5/13
With opposite = 5 and adjacent = 12, hypotenuse = 13; sin θ = 5/13.
Question 4: The horizontal shift (phase shift) in y = sin(x + 45°) is:
- 45° to the left (Correct answer)
- 45° to the right
- 45 units up
- 45 units down
Correct answer: 45° to the left
Adding 45° inside the function shifts the graph 45° to the left.
Question 5: Which of the following is NOT a correct reduction formula?
- sin(180° + θ) = sin θ (Correct answer)
- cos(180° + θ) = −cos θ
- tan(180° + θ) = tan θ
- sin(360° − θ) = −sin θ
Correct answer: sin(180° + θ) = sin θ
sin(180° + θ) = −sin θ (Quadrant III, sine is negative), not +sin θ.
Question 6: The value of sin(−60°) is:
- −√3/2 (Correct answer)
- √3/2
- 1/2
- −1/2
Correct answer: −√3/2
Sine is an odd function: sin(−60°) = −sin 60° = −√3/2.
Question 7: In a right-angled triangle, the angle of elevation from a point 20 m from the base of a tower to its top is 45°. The height of the tower is:
- 20 m (Correct answer)
- 20√2 m
- 10 m
- 40 m
Correct answer: 20 m
tan 45° = height/20 → height = 20 × 1 = 20 m.
NBT NBT Mathematics: Trigonometry 5
What is the range of y = sin x?