Lesson E4

E4 Secant, cosecant, cotangent and inverse trigonometric functions Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E4, Secant, cosecant, cotangent and inverse trigonometric functions: 20 multiple choice questions for the AQA Maths (7357), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. Which expression defines sec x in terms of cos x?

    • sec x = cos x
    • sec x = 1/sin x
    • sec x = 1/cos x
    • sec x = sin x/cos x

  2. Which expression defines cosec x in terms of sin x?

    • cosec x = 1/sin x
    • cosec x = sin x
    • cosec x = 1/cos x
    • cosec x = cos x/sin x

  3. Which expression defines cot x in terms of sin x and cos x?

    • cot x = 1/(sin x cos x)
    • cot x = sin x/cos x
    • cot x = 1/cos^2 x
    • cot x = cos x/sin x

  4. What is the domain of y = arcsin x?

    • -1 <= x <= 1
    • 0 <= x <= 1
    • -pi/2 <= x <= pi/2
    • All real values of x

  5. What is the range of y = arccos x?

    • 0 <= y <= 2 pi
    • 0 <= y <= pi
    • -pi <= y <= pi
    • -pi/2 <= y <= pi/2

  6. What is the range of y = arctan x?

    • -pi/2 < y < pi/2
    • 0 <= y <= pi
    • All real values of y
    • -1 <= y <= 1

  7. What is the principal value of arcsin(1)?

    • pi/2
    • pi/4
    • 0
    • pi

  8. Evaluate arccos(-1/2), giving the principal value.

    • -pi/3
    • pi/3
    • 5 pi/6
    • 2 pi/3

  9. Evaluate sec(pi/3).

    • 2
    • 2/sqrt(3)
    • 1/2
    • sqrt(3)/2

  10. Evaluate cot(pi/4).

    • 1
    • 0
    • 1/sqrt(3)
    • sqrt(3)

  11. Evaluate cosec(5 pi/6).

    • 2
    • -2
    • sqrt(3)
    • 1/2

  12. Evaluate arctan(sqrt(3)), giving the principal value.

    • pi/6
    • 2 pi/3
    • pi/3
    • pi/4

  13. What is the principal value of arcsin(sin(3 pi/4))?

    • pi/2
    • -pi/4
    • 3 pi/4
    • pi/4

  14. For which values of x is sec x undefined?

    • x = n pi for integer n, where sin x = 0
    • No real values; sec x is defined for all real x
    • x = 0 only
    • x = (2n+1) pi/2 for integer n, where cos x = 0

  15. For which values of x is cot x undefined?

    • x = n pi/2 for integer n
    • x = 0 only
    • x = n pi for integer n, where sin x = 0
    • x = (2n+1) pi/2 for integer n, where cos x = 0

  16. The graph of y = arccos x is obtained from the graph of y = cos x (0 <= x <= pi) by which transformation?

    • Reflection in the line y = x
    • Translation by pi/2 in the x direction
    • Reflection in the y-axis
    • Reflection in the x-axis

  17. Given cot theta = 2 with theta in (0, pi/2), find cosec theta.

    • sqrt(5)
    • sqrt(3)
    • 2
    • 5

  18. Given sec x = 3 with x in the first quadrant, find cos x.

    • 3
    • 1/sqrt(2)
    • 1/3
    • 2 sqrt(2)

  19. Given tan x = 3/4 with x acute, find cosec x.

    • 3/4
    • 5/3
    • 4/3
    • 5/4

  20. What is the exact value of arcsec(2), giving the principal value?

    • pi/2
    • pi/6
    • pi/3
    • 2 pi/3

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