What makes a trigonometric equation a "further" one?

It involves reciprocal or inverse functions, or needs a compound or double angle formula before it can be reduced. The solving itself is unchanged; it is getting to that point that is harder.

With several identities available, how do you decide which one to use on an equation?

Look at what the equation contains and at what has to go. An identity earns its place if it removes a term, or brings two different angles down to one.

A LevelMathsEdexcelPureFlashcardsTrigonometryFurther Trigonometric Equations

Further Trigonometric Equations (Edexcel A Level Maths: Pure): Flashcards

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FrontStrategy for Further Trigonometric Equations
What makes a trigonometric equation a "further" one?

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Cards in this collection (5)

What makes a trigonometric equation a "further" one?
It involves reciprocal or inverse functions, or needs a compound or double angle formula before it can be reduced.
The solving itself is unchanged; it is getting to that point that is harder.
With several identities available, how do you decide which one to use on an equation?
Look at what the equation contains and at what has to go.
An identity earns its place if it removes a term, or brings two different angles down to one.
An equation contains both $\sin 2 x$ and $\sin x$ . What has to happen first?
Replace $\sin 2 x$ with $2 \sin x \cos x$ , so that every term is in the same angle.
An equation mixing two different angles cannot be solved until they agree.
You have solved an equation for $2 x$ over a transformed interval. What is the last step?
Halve every solution, to convert back from $2 x$ to $x$ .
Transforming the interval was what stopped solutions being lost; converting back is what makes the answers answer the question asked.
True or False?
A further trigonometric equation finishes with the same step as a simple one.
True.
All the extra work is in the reducing; the final step is always $\sin x = k$ , $\cos x = k$ or $\tan x = k$ .
What changes at this level is how much has to happen before you get there.

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