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CAIE A Level Mathematics 9709

Trigonometry (AS) questions

Exam-style questions on Trigonometry (AS), 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. 2 marksFoundationAn acute angle x satisfies cos x = (55)/(73). Find the exact value of sin x as a fraction.
  2. 1 markFoundationFind the exact value of cos 30^°.
  3. 1 markFoundationFind the exact value of sin 60^°.
  4. 2 marksStandardAn acute angle x satisfies sin x = (1)/(100). Find cosec x.
  5. 2 marksStandardAn acute angle x satisfies cos x = (1)/(8). Find sec x.
  6. 2 marksStandardAn acute angle x satisfies tan x = (5)/(25). Find cot x.
  7. 2 marksStandardAn acute angle x satisfies sin x = (12)/(13). Find the exact value of tan x as a fraction.
  8. 2 marksStandardAn acute angle x satisfies sin x = (36)/(45). Find the exact value of cos x as a fraction.
  9. 2 marksStandardSolve tan x = tan 25^° for 0^° ≤ x < 360^°. Give your answers in degrees.
  10. 2 marksStandardSolve 5sin x = 5sin 40^° for 0^° ≤ x < 360^°.
  11. 2 marksStandardSolve cos x = cos 70^° for 0^° ≤ x < 360^°. Give your answers in degrees.
  12. 3 marksStandardSimplify the expression: ( 5 - 5 sin^2 x)/(cos x).
  13. 3 marksStandardGiven that sin x = (12)/(15) and x lies in quadrant 1, find the exact value of cos x.
  14. 2 marksStandardSolve sin x = sin 25^° for 0^° ≤ x < 360^°. Give your answers in degrees.