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Linear Trigonometric Equations (CIE A Level Maths: Pure 1)
Revision Note
Linear Trigonometric Equations
Solving 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?
What about more complicated trig 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
Examiner Tip
- 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
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