10 questions · Form 5 Additional Mathematics Bab 6: Trigonometric Functions
What is the period of the function y = 3 cos (2x) + 1?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. What is the period of the function y = 3 cos (2x) + 1?
Answer: A
Period for cosine = 360° / b. Here b = 2, so Period = 360° / 2 = 180°.
2. 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.
3. Given that sin A = 35 and A is an acute angle, find the value of cos 2A.
Answer: A
cos 2A = 1 - 2 sin² A = 1 - 2(35)² = 1 - 2(925) = 1 - 1825 = 725.
4. Solve cos θ = 0 for 0° ≤ θ ≤ 360°.
Answer: A
On the unit circle, cos θ = 0 at θ = 90° and θ = 270°.
5. Simplify sin 2x1 + cos 2x.
Answer: A
sin 2x1 + cos 2x = 2 sin x cos x1 + 2 cos² x - 1 = 2 sin x cos x2 cos² x = sin x / cos x = tan x.
6. If cos θ = -12 and θ lies in Quadrant III, find the exact value of θ.
Answer: A
Reference angle α = cos⁻¹(12) = 60°. In Quadrant III, θ = 180° + 60° = 240°.
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. Express sec² θ - tan² θ in its simplest form.
Answer: A
From the identity 1 + tan² θ = sec² θ, rearranging gives sec² θ - tan² θ = 1.
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. Find the amplitude of the function y = -4 sin (3x) - 2.
Answer: A
Amplitude is the absolute value of coefficient a. Amplitude = |-4| = 4.