Linear Trigonometric Equations (Edexcel AS Maths): Revision Note
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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 Tips and Tricks
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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