10 questions · Form 5 Mathematics Bab 6: Ratios and Graphs of Trigonometric Functions
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Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. State the maximum and minimum values of the function y = 2 sin x - 1.
Answer: A
Maximum = 2(1) - 1 = 1. Minimum = 2(-1) - 1 = -3.
2. Solve tan x = 0 for 0° ≤ x ≤ 360°.
Answer: A
tan x = sin x / cos x = 0 when sin x = 0, which occurs at x = 0°, 180°, and 360°.
3. If tan θ = 34 and θ is in Quadrant III, find the value of sin θ.
Answer: A
In Q III, opposite = -3, adjacent = -4, hypotenuse = √(-3)² + (-4)² = 5. sin θ = opposite / hypotenuse = -35.
4. Calculate the acute reference angle for θ = 210°.
Answer: A
210° is in Quadrant III. The reference angle α = θ - 180° = 210° - 180° = 30°.
5. Which trigonometric graph has vertical asymptotes at x = 90° and x = 270° for 0° ≤ x ≤ 360°?
Answer: A
tan(90°) and tan(270°) are undefined (yx where x=0), creating vertical asymptotes in y = tan x.
6. What is the amplitude of the trigonometric function y = 3 cos(2x) + 1?
Answer: A
In y = a cos(bx) + c, the amplitude is |a| = 3.
7. At which of the following angles in 0° ≤ x ≤ 360° does y = cos x reach its minimum value?
Answer: C
cos(180°) = -1, which is the minimum value for the cosine function.
8. Given that tan θ = -1 and 90° ≤ θ ≤ 180°, find the angle θ.
Answer: B
tan θ is negative in Quadrant II. Reference angle α = tan⁻¹(1) = 45°. Thus θ = 180° - 45° = 135°.
9. If sin θ = 0.6 and θ is an obtuse angle (90° < θ < 180°), what is the value of cos θ?
Answer: A
In Quadrant II, cos θ is negative. Using sin²θ + cos²θ = 1 => cos θ = -√1 - 0.6² = -√0.64 = -0.8.
10. What is the exact value of tan(315°)?
Answer: B
315° is in Quadrant IV (tangent is negative). Reference angle = 360° - 315° = 45°. tan(315°) = -tan(45°) = -1.