Lesson E1

E1 Trigonometric definitions, sine and cosine rules, radians Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson E1, Trigonometric definitions, sine and cosine rules, radians: 20 multiple choice questions for the AQA Maths (7357), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. In a right-angled triangle, what is sin of an angle?

    • Opposite over adjacent
    • Adjacent over hypotenuse
    • Hypotenuse over opposite
    • Opposite over hypotenuse

  2. Which expression is the sine rule in triangle ABC?

    • a/sin A = b/sin B = c/sin C
    • a^2 = b^2 + c^2 - 2bc cos A
    • a/cos A = b/cos B = c/cos C
    • sin A/a = b sin B

  3. Which expression is the cosine rule in triangle ABC?

    • a^2 = b^2 + c^2 + 2bc cos A
    • a^2 = b^2 + c^2 - bc cos A
    • a = b + c - cos A
    • a^2 = b^2 + c^2 - 2bc cos A

  4. What is the area of a triangle with two sides a and b enclosing angle C?

    • (1/2)(a + b) sin C
    • (1/2)ab cos C
    • (1/2)ab sin C
    • ab sin C

  5. What is 180 degrees in radians?

    • 2 pi
    • pi/2
    • 180
    • pi

  6. What is the arc length s of a circle of radius r subtending an angle theta in radians?

    • s = r^2 theta
    • s = theta/r
    • s = 2 pi r
    • s = r theta

  7. What is the area of a sector of radius 6 cm and angle 1 radian?

    • 3 cm^2
    • 36 cm^2
    • 18 cm^2
    • 6 pi cm^2

  8. What is the exact area of a triangle with sides 7 and 5 enclosing an angle of 60 degrees?

    • 35/4
    • 35 sqrt(2)/4
    • 35 sqrt(3)/4
    • 35 sqrt(3)/2

  9. In a triangle, A = 30 degrees, a = 10 and B = 50 degrees. What is b to one decimal place?

    • 7.7
    • 20.0
    • 12.9
    • 15.3

  10. A triangle has sides b = 8, c = 5 and a = 7. What is angle A?

    • 60 degrees
    • 45 degrees
    • 120 degrees
    • 30 degrees

  11. A circle of radius 10 cm subtends an angle of 0.6 radians at the centre. What is the arc length?

    • 60 cm
    • 0.06 cm
    • 16 cm
    • 6 cm

  12. What is 150 degrees in radians?

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

  13. A sector has radius 3 and angle 2 pi/3. What is its area?

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

  14. In a triangle with sides 3, 4 and 5, what is the largest angle?

    • 90 degrees
    • 45 degrees
    • 105 degrees
    • 60 degrees

  15. What is the exact value of cos(pi/3)?

    • sqrt(3)/2
    • 1
    • 0
    • 1/2

  16. Two sides of a triangle are 3 and 5 and the included angle is 120 degrees. What is the third side?

    • sqrt(19)
    • 7
    • sqrt(34)
    • 8

  17. What is the area of a triangle with sides 4 and 6 enclosing 30 degrees?

    • 3
    • 6
    • 12
    • 6 sqrt(3)

  18. What is the exact value of sin(5 pi/6)?

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

  19. A sector has area 12 and radius 4. What is its angle in radians?

    • 0.75 radians
    • 1.5 radians
    • 3 radians
    • 6 radians

  20. Two sides of a triangle are 10 m and 14 m with an included angle of 60 degrees. What is the third side?

    • About 11.2 m
    • About 14 m
    • About 12.5 m
    • About 24 m

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