10 questions · Form 5 Mathematics Bab 6: Ratios and Graphs of 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. In which quadrant are both sine and tangent negative, while cosine is positive?
Answer: A
By the ASTC rule, in Quadrant IV only cosine is positive; sine and tangent are negative.
2. 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.
3. 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.
4. Calculate the value of sin(150°) + cos(60°).
Answer: A
sin(150°) = sin(30°) = 12. cos(60°) = 12. Total = 12 + 12 = 1.
5. Which of the following points lies on the curve y = cos x?
Answer: A
cos(90°) = 0, so the point (90°, 0) lies on y = cos x.
6. 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°.
7. 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.
8. 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.
9. 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.
10. What is the period of the tangent graph y = tan(3x)?
Answer: A
The period of tan(bx) is 180° / b = 180° / 3 = 60°.