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:
- 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!).