AQA A Level Maths: Pure复习笔记5.7.1 Strategy for Further Trigonometric Equations

Strategy for Further Trigonometric Equations

How to approach solving 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 Tip

  • 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