CAIE A-Level Mathematics 1.5.5 Trigonometric Equations

CAIE A-Level Mathematics 1.5.5 Trigonometric Equations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise reducing trigonometric equations with identities or substitutions, solving for the trig ratio and generating every valid angle in the specified interval.

How this is tested

  • use an identity to rewrite the equation in one trig ratio before solving its quadratic
  • find the reference angle and select every quadrant consistent with the signed trig value
  • check endpoints and the stated degree or radian interval, rejecting duplicates and extra roots

Question 1

[Maximum number: 4]

Solve the equation 6 sin(theta)=1+2/sin(theta) for -180 degrees < theta < 180 degrees.