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Quiz Chapter 6: Ratios and Graphs of Trigonometric Functions

10 questions · Form 5 Mathematics Bab 6: Ratios and Graphs of Trigonometric Functions

Question 1 of 10Score: 0

Calculate the acute reference angle for θ = 210°.

Full Question List & Answer Key

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°.

  1. A. 30°
  2. B. 60°
  3. C. 150°
  4. D. 40°
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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°.

  1. A. 60° and 300°
  2. B. 60° and 120°
  3. C. 120° and 240°
  4. D. 30° and 330°
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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?

  1. A. (90°, 0)
  2. B. (0°, 0)
  3. C. (180°, 1)
  4. D. (270°, -1)
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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?

  1. A. 3
  2. B. 2
  3. C. 1
  4. D. 4
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Answer: A

In y = a cos(bx) + c, the amplitude is |a| = 3.

5. Calculate the value of sin(150°) + cos(60°).

  1. A. 1
  2. B. 0
  3. C. √3
  4. D. 12
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Answer: A

sin(150°) = sin(30°) = 12. cos(60°) = 12. Total = 12 + 12 = 1.

6. Solve tan x = 0 for 0° ≤ x ≤ 360°.

  1. A. 0°, 180°, and 360°
  2. B. 90° and 270°
  3. C. 0° and 360° only
  4. D. 180° only
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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°?

  1. A. y = tan x
  2. B. y = sin x
  3. C. y = cos x
  4. D. y = 2 cos x
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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.

  1. A. -35
  2. B. 35
  3. C. -45
  4. D. 45
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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?

  1. A. Shifts the graph vertically upwards or downwards
  2. B. Alters the period of the graph
  3. C. Increases the amplitude
  4. D. Flips the graph horizontally
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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°)?

  1. A. -12
  2. B. 12
  3. C. -√32
  4. D. √32
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Answer: A

120° is in Quadrant II where cosine is negative. Reference angle = 180° - 120° = 60°. Thus, cos(120°) = -cos(60°) = -12.

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