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Trigonometry Practice Test: printable

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Trigonometry Practice Test

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28 questions. Calculator allowed. Show your working. steplyclass.com/trigonometry/practice-test/

  1. 1

    Convert 30° to radians

    Answer: ____________________

  2. 2

    Convert 5π/12 to degrees

    Answer: ____________________

  3. 3

    Arc length radius 6, angle 2π/3
    1. A) s ≈ 6
    2. B) s ≈ 12.57
    3. C) s ≈ 125.7
    4. D) s ≈ 1.257

  4. 4

    Sector area radius 12, angle 5π/6

    Answer: ____________________

  5. 5

    Exact value of sin 30°
    1. A) 1
    2. B) 12
    3. C) 2
    4. D) √32

  6. 6

    Exact value of sin 270°

    Answer: ____________________

  7. 7

    Exact value of cos 150°

    Answer: ____________________

  8. 8

    Exact value of sin 420°

    Answer: ____________________

  9. 9

    Calculate sin−1(12)

    Answer: ____________________

  10. 10

    Calculate tan−1(√33) in degrees

    Answer: ____________________

  11. 11

    Prove sin2 x + cos2 x = 1

    Answer: ____________________

  12. 12

    Simplify (1 + tan2 x) cos2 x

    Answer: ____________________

  13. 13

    Exact value of sin 75°

    Answer: ____________________

  14. 14

    Calculate sin 100° cos 55° − cos 100° sin 55°

    Answer: ____________________

  15. 15

    Solve sin 2θ when sin θ = 35, θ in quadrant I
    1. A) 25
    2. B) 65
    3. C) 16
    4. D) 2425

  16. 16

    cos 2θ when tan θ = −125, θ in quadrant IV

    Answer: ____________________

  17. 17

    Solve 2 sin x − 1 = 0
    1. A) x = 30°, 150°
    2. B) 150°
    3. C) x = −30°, −150°
    4. D) x = 30°

  18. 18

    Solve 2 cos2 x + cos x = 0

    Answer: ____________________

  19. 19

    Solve sin 2x = 12

    Answer: ____________________

  20. 20

    Solve sin 3x = 1

    Answer: ____________________

  21. 21

    Solve 2 sin2 x − sin x − 1 = 0
    1. A) x = 90°
    2. B) x = 90°, 210°, 330°
    3. C) x = −90°, 210°, 330°
    4. D) x = −90°, −210°, −330°

  22. 22

    Solve 2 cos2 x + cos x − 1 = 0 on 0 to 2π

    Answer: ____________________

  23. 23

    Triangle A = 40°, B = 60°, a = 8, find b
    1. A) b ≈ 108
    2. B) b ≈ 10.8
    3. C) b ≈ 1.08

  24. 24

    Triangle A = 50°, a = 12, b = 9, find B

    Answer: ____________________

  25. 25

    Triangle a = 5, b = 7, C = 60°, find c
    1. A) c ≈ 6.2
    2. B) c ≈ 1.4
    3. C) c ≈ 39
    4. D) c ≈ 35

  26. 26

    Triangle a = 8 cm, b = 6 cm, c = 5 cm, find B

    Answer: ____________________

  27. 27

    Find the area of triangle a = 8, b = 5, C = 30°.

    Answer: ____________________

  28. 28

    Find the area of triangle a = 20, b = 3, C = 100°.

    Answer: ____________________

Answer key

  1. π/6
  2. 75°
  3. B s ≈ 12.57
  4. A ≈ 188.50
  5. B 12
  6. −1
  7. −√32
  8. √32
  9. π/6
  10. 30°
  11. 1
  12. 1
  13. (√6 + √2)/4
  14. √22
  15. D 2425
  16. −119169
  17. A x = 30°, 150°
  18. x = 90°, 120°, 240°, 270°
  19. x = 15°, 75°, 195°, 255°
  20. x = 30°, 150°, 270°
  21. B x = 90°, 210°, 330°
  22. x = π/3, π, 5π/3
  23. B b ≈ 10.8
  24. B ≈ 35.1°
  25. A c ≈ 6.2
  26. B ≈ 48.5°
  27. A = 10
  28. A ≈ 29.5

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