10 questions · Form 5 Mathematics Bab 6: Ratios and Graphs of Trigonometric Functions
Calculate the acute reference angle for θ = 210°.
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Calculate the acute reference angle for θ = 210°.
Answer: A
210° is in Quadrant III. The reference angle α = θ - 180° = 210° - 180° = 30°.
2. Solve the equation 2 cos x = 1 for 0° ≤ x ≤ 360°.
Answer: A
cos x = 12 (positive in Q I and Q IV). Reference angle = 60°. Q I: x = 60°; Q IV: x = 360° - 60° = 300°.
3. 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.
4. 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.
5. Calculate the value of sin(150°) + cos(60°).
Answer: A
sin(150°) = sin(30°) = 12. cos(60°) = 12. Total = 12 + 12 = 1.
6. 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°.
7. 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.
8. 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.
9. What is the effect of 'c' in the transformation y = a sin(bx) + c on the basic sine graph?
Answer: A
The constant 'c' represents a vertical shift of the baseline of the trigonometric curve.
10. What is the exact value of cos(120°)?
Answer: A
120° is in Quadrant II where cosine is negative. Reference angle = 180° - 120° = 60°. Thus, cos(120°) = -cos(60°) = -12.