10 questions · Form 5 Additional Mathematics Bab 6: Trigonometric Functions
Which of the following is equivalent to csc θ?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Which of the following is equivalent to csc θ?
Answer: A
By definition, cosecant (csc θ) is the reciprocal of sine, so csc θ = 1 / sin θ.
2. Which identity is equivalent to cos 2A?
Answer: A
Double angle formula for cosine: cos 2A = cos² A - sin² A = 2 cos² A - 1 = 1 - 2 sin² A.
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. 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.
5. Find the amplitude of the function y = -4 sin (3x) - 2.
Answer: A
Amplitude is the absolute value of coefficient a. Amplitude = |-4| = 4.
6. 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.
7. 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°.
8. 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°.
9. Simplify (1 - cos² θ) / sin θ.
Answer: A
Using Pythagorean identity sin² θ + cos² θ = 1 => 1 - cos² θ = sin² θ. Therefore, sin² θ / sin θ = sin θ.
10. 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.