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CAIE A Level Mathematics 9709

Trigonometry (A2) questions

Exam-style questions on Trigonometry (A2), ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 1 markFoundationFor 5sin x + 1cos x = Rsin(x + α), find R^2.
  2. 1 markFoundationGiven cos x = (9)/(11), write sec x as a fraction.
  3. 1 markFoundationGiven sin x = (9)/(11), write cosec x as a fraction.
  4. 3 marksFoundationUse a compound-angle formula to find the exact value of sin(60^° - 30^°). Give your answer as a decimal.
  5. 2 marksStandardWrite 15cos x + 20sin x as Rcos(x - α) with R 0 and 0 < α < 90^°. State R.
  6. 3 marksStandardExpress 5 sin θ - 12 cos θ in the form R sin(θ - α), where R 0 and 0 < α < π/2. Give your answer as an exact expression in terms of θ.
  7. 3 marksStandardAn equation reduces to sin x = sin 20^°. Solve for 0^° ≤ x < 360^°.
  8. 2 marksStandardFind the minimum value of 18sin x + 24cos x.
  9. 3 marksStandardThe equation sin 2x = 2cos 40^° sin x reduces to cos x = cos 40^°. Solve for 0^° ≤ x < 360^°.
  10. 2 marksStandardExpress 16sin x + 30cos x in the form Rsin(x + α) with R 0. Find R.
  11. 2 marksStandardFind the maximum value of 30sin x + 16cos x.
  12. 3 marksStandardGiven that sinθ = frac35 and that θ is obtuse (so cosθ is negative), find the following exact values.