Strategy for Trigonometric Equations (DP IB Analysis & Approaches (AA)): Revision Note

Strategy for trigonometric equations

How do I approach solving trig equations?

• Check the coefficient of θ

  • If there are different multiples of θ

    • you will need to use the double angle identities to get everything in terms of the same multiple of θ

  • If it is a function of θ, e.g. 2x – 15

    • you will need to make a substitution first

• Check how many trigonometric functions are included

  • If there is only one

    • try to rearrange everything to bring it to one side

    • you may need to factorise

  • If there is more than one

    • try to use the Pythagorean identities and the tan identity

    • you should be able to use identities to reduce everything to just one simple trig function

• Check what type of expression you end up with

  • If it is a linear equation

    • you should be able to rearrange and solve it

  • If it is a quadratic equation

    • solve the quadratic first and check whether they are valid solutions

    • remember solutions to sin x = k and cos x = k only exist for -1 ≤ k ≤ 1 whereas solutions to tan x = k exist for all values of k

    • then solve each resulting simple trig equations

• The flow chart below is a helpful summary of the process