10 questions · Form 5 Additional Mathematics Bab 6: Trigonometric Functions
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. State the maximum value of y = 5 cos (x) - 3.
Answer: A
Maximum value of cos x is 1. So Max y = 5(1) - 3 = 2.
2. Solve cos θ = 0 for 0° ≤ θ ≤ 360°.
Answer: A
On the unit circle, cos θ = 0 at θ = 90° and θ = 270°.
3. Solve 2 sin θ = 1 for 0° ≤ θ ≤ 360°.
Answer: A
sin θ = 12. Reference angle α = 30°. Sine is positive in Quadrants I and II. θ = 30° and (180° - 30°) = 150°.
4. The graph of y = a sin (bx) has 3 complete cycles in 360°. What is the value of b?
Answer: A
The number of complete cycles in 360° (or 2π) is directly given by the parameter b. Thus, b = 3.
5. Find the value of tan 105° using compound angle formulae.
Answer: A
tan 105° = tan (60° + 45°) = tan 60° + tan 45°1 - tan 60° tan 45° = √3 + 11 - √3 = -2 - √3.
6. Given tan A = 43 where A is acute, find sec A.
Answer: A
1 + tan² A = sec² A => 1 + (43)² = 1 + 169 = 259. Since A is acute, sec A = √(259) = 53.
7. Given tan θ = -1 and 90° ≤ θ ≤ 180°, find the value of θ.
Answer: A
Reference angle α = 45°. Since θ is in Quadrant II (90° ≤ θ ≤ 180°), θ = 180° - 45° = 135°.
8. Simplify sin A cos B + cos A sin B.
Answer: A
This is the addition expansion formula for sine: sin (A + B) = sin A cos B + cos A sin B.
9. What is the period of y = 2 tan (3x)?
Answer: A
Period for tangent = 180° / b. Here b = 3, so Period = 180° / 3 = 60°.
10. Express 2 sin 15° cos 15° as a single trigonometric ratio and find its exact value.
Answer: A
Using double angle formula 2 sin A cos A = sin 2A: 2 sin 15° cos 15° = sin (2 × 15°) = sin 30° = 12.