Strategy for Further Trigonometric Equations (Cambridge International A-Level Mathematics)

Strategy for further trigonometric equations

How do I solve harder trig equations?

• You can solve harder trig equations, such as those involving reciprocal and inverse functions in a variety of different ways

  • Using further trigonometric identities
  • Using compound or double angle formulas
  • Factorising quadratic trig equations
  • Then finding all solutions using CAST or sketching graphs

• The final rearranged equation you solve will involve sin, cos or tan – don’t try to solve an equation with cosec, sec, or cot directly

• If you’re having trouble solving a trig equation, this flowchart might help:

Exam Hint

• Try to use identities and formulas to reduce the equation into its simplest terms.
• Don’t forget to check the function range and ensure you have included all possible solutions.
• If the question involves a function of x or θ ensure you transform the range first (and ensure you transform your solutions back again at the end!).

Worked Example