Linear Trigonometric Equations (Edexcel IAL Maths)

Spec point — 6.2

Linear trigonometric equations

How do I solve linear trigonometric equations?

• You should have already seen two ways to solve linear trig equations

  • By sketching the graph (see Graphs of Trigonometric Functions) you can read off all the solutions in a given range (or interval)
  • By using trigonometric identities you can simplify harder equations

• Another way to find solutions is by using the CAST diagram which shows where each function has positive solutions

• You may be asked to use degrees or radians to solve trigonometric equations

  • Make sure your calculator is in the correct mode

  • Remember common angles

    • 90° is ½π radians
    • 180° is π radians
    • 270° is 3π/2 radians
    • 360° is 2π radians

How do I use the CAST diagram?

How do I solve more complicated trigonometric equations?

• Some trig equations could involve a function of x or θ (see Transformations of Trigonometric Functions)
• Functions could be in two forms, either y = sin(θ ± k) or y = sin kθ
• An easy way to solve an equation involving sin, cos or tan of (θ± k) or kθ is by transforming the range of the question

Exam Hint

• Your calculator will only give you the principal value and you need to find all other solutions for the given interval.
• Also, remember the CAST diagram only gives you some solutions, so again you may need to find more depending on the given interval.
• It is entirely up to you how you solve a trig equation, but some ways are more helpful than others depending on the type of equation you are trying to solve

Worked Example