PAF Initial Test Mathematics: Trigonometric Functions MCQs

Practice Trigonometric Functions MCQs for PAF Initial Test Mathematics — topic-wise sets with solved answers.

PAF Initial Test Mathematics: Trigonometric Functions MCQs — sample questions

  1. Question 1

    Q1. What is the period of sin(2x) + cos(3x)?

    • A) 2π
    • B) π
    • C) 2π/3
    • D) LCM of 2π/2 and 2π/3

    Answer: LCM of 2π/2 and 2π/3

    Explanation: The period of sin(ax) + cos(bx) is LCM of 2π/a and 2π/b, so here it's LCM of 2π/2 and 2π/3.

  2. Question 2

    Q2. If sin(x) = 1/2, what is cos(2x)?

    • A) 1/2
    • B) -1/2
    • C) 1
    • D) 0

    Answer: 1/2

    Explanation: Using cos(2x) = 1 - 2sin²x with sin x = 1/2 gives cos(2x) = 1/2.

  3. Question 3

    Q3. The graph of y = sin(x) is symmetric about?

    • A) x-axis
    • B) y-axis
    • C) origin
    • D) line x = π/2

    Answer: origin

    Explanation: The sine function is odd, so its graph is symmetric about the origin.

  4. Question 4

    Q4. What is the amplitude of 3sin(x) + 4cos(x)?

    • A) 3
    • B) 4
    • C) 5
    • D) 7

    Answer: 5

    Explanation: The amplitude of asin(x) + bcos(x) is √(a² + b²), so here it's √(3² + 4²) = √(9 + 16) = √25 = 5.

  5. Question 5

    Q5. The range of f(x) = 2sin(x) + 1 is?

    • A) [1, 3]
    • B) [-1, 3]
    • C) [0, 2]
    • D) [-2, 2]

    Answer: [-1, 3]

    Explanation: The range of sin(x) is [-1, 1], so the range of 2sin(x) is [-2, 2] and the range of 2sin(x) + 1 is [-2 + 1, 2 + 1] = [-1, 3].

  6. Question 6

    Q6. If tan(x) = 1, what is x in 1 / 2 radians?

    • A) π/4
    • B) π/2
    • C) 3π/4
    • D) π

    Answer: π/4

    Explanation: tan(π/4) = 1, so x = π/4 radians.

  7. Question 7

    Q7. What is the value of sin(π/6) + cos(π/3)?

    • A) 1
    • B) 1/2
    • C) 3/2
    • D) 1/4

    Answer: 1

    Explanation: sin(π/6) = 1/2 and cos(π/3) = 1/2, so the sum equals 1.

  8. Question 8

    Q8. The period of cos(x) + sin(x) is?

    • A) π
    • B) 2π
    • C) π/2
    • D) 3π/2

    Answer: 2π

    Explanation: Both sin(x) and cos(x) have a period of 2π, so their sum also has a period of 2π.

  9. Question 9

    Q9. If f(x) = sin(x), what is f(π/2 + x)?

    • A) sin(x)
    • B) cos(x)
    • C) -sin(x)
    • D) -cos(x)

    Answer: cos(x)

    Explanation: Using the identity sin(π/2 + x) = cos(x).

  10. Question 10

    Q10. The maximum value of sin(x) + cos(x) is?

    • A) 1
    • B) √2
    • C) 2
    • D) 1/√2

    Answer: √2

    Explanation: The maximum value of asin(x) + bcos(x) is √(a² + b²), so here it's √(1² + 1²) = √2.

  11. Question 11

    Q11. What is the minimum value of 2cos(x) - 1?

    • A) -3
    • B) -1
    • C) 1
    • D) 3

    Answer: -3

    Explanation: The minimum value of cos(x) is -1, so the minimum value of 2cos(x) - 1 is 2(-1) - 1 = -3.

  12. Question 12

    Q12. The graph of y = cos(x) is symmetric about?

    • A) x-axis
    • B) y-axis
    • C) origin
    • D) line x = π/2

    Answer: y-axis

    Explanation: The cosine function is even, so its graph is symmetric about the y-axis.

  13. Question 13

    Q13. What is the amplitude of 2sin(3x)?

    • A) 1
    • B) 2
    • C) 3
    • D) 6

    Answer: 2

    Explanation: The amplitude of asin(bx) is |a|, so here it's |2| = 2.

  14. Question 14

    Q14. The range of f(x) = cos(x) - 2 is?

    • A) [-3, -1]
    • B) [-1, 1]
    • C) [0, 2]
    • D) [-2, 2]

    Answer: [-3, -1]

    Explanation: The range of cos(x) is [-1, 1], so the range of cos(x) - 2 is [-1 - 2, 1 - 2] = [-3, -1].

  15. Question 15

    Q15. What is the value of sin(π/3) + cos(π/6)?

    • A) √3
    • B) 1 + √3/2
    • C) 3/2
    • D) √3/2 + 1

    Answer: √3

    Explanation: sin(π/3) = √3/2 and cos(π/6) = √3/2, so the sum equals √3.

  16. Question 16

    Q16. The period of sin(2x) is?

    • A) π
    • B) 2π
    • C) π/2
    • D) 3π/2

    Answer: π

    Explanation: The period of sin(ax) is 2π/a, so here it's 2π/2 = π.

  17. Question 17

    Q17. If f(x) = cos(x), what is f(π + x)?

    • A) cos(x)
    • B) -cos(x)
    • C) sin(x)
    • D) -sin(x)

    Answer: -cos(x)

    Explanation: Using the identity cos(π + x) = -cos(x).

  18. Question 18

    Q18. The maximum value of 3sin(x) is?

    • A) 1
    • B) 3
    • C) 2
    • D) 4

    Answer: 3

    Explanation: The maximum value of sin(x) is 1, so the maximum value of 3sin(x) is 3(1) = 3.

  19. Question 19

    Q19. What is the period of the function y = sin(3x)?

    • A) 2π/3
    • B) 2π
    • C) π/3
    • D) 3π

    Answer: 2π/3

    Explanation: The period of sin(ax) is 2π/a, so for sin(3x), it is 2π/3.

  20. Question 20

    Q20. The graph of y = cos(x) is symmetric about which line?

    • A) x = 0
    • B) y = 0
    • C) x = π/2
    • D) y = 1

    Answer: x = 0

    Explanation: y = cos(x) is an even function, so it is symmetric about the y-axis, x = 0.

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