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C3 Trig Identity Explanation HELP!!

Hi guys

For Edexcel maths, in the formula book under C3 there are these identities:
c3 weird trig identities.PNG

I have no idea what they are used for, or how to use them.

I'd be grateful for an explanation.

In this pack of questions: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/Edexcel-Set-1/C3%20Trigonometry%20-%20Trigonometric%20equations.pdf, Q18 (d) quotes one of these types of identities that have to be used to find the values of x.

No idea what to do ! Cheeeers.
(edited 5 years ago)
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Avatar for mqb2766
mqb2766
21
They underpin the double angle formulae, examples of which are
http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-doubleangle-2009-1.pdf
and a fair number of examples of the addition formulae are
http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-addnformulae-2009-1.pdf

Like most trig relationships, they're used to transform the problem into a form you want ... whatever that is.
Original post by 221Breezeblocks
Hi guys

For Edexcel maths, in the formula book under C3 there are these identities:
c3 weird trig identities.PNG

I have no idea what they are used for, or how to use them.

I'd be grateful for an explanation.

In this pack of questions: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/Edexcel-Set-1/C3%20Trigonometry%20-%20Trigonometric%20equations.pdf, Q18 (d) quotes one of these types of identities that have to be used to find the values of x.

No idea what to do ! Cheeeers.


They're given in the formulae booklet, but you don't need to know them and won't be required to use them; there is no mention of them whatsoever on the syllabus. The reason for this is that the formulae booklet was produced in 2004, when the system of C, FP, M, S, and D modules was introduced, and the booklet hasn't been updated since then as the syllabus has changed.

Nevertheless, if you do want to learn about them: for Q18(d), we get 1/cos(x) + sqrt(3)/sin(x) = 4, so multiplying by sin(x)cos(x) gives sin(x) + sqrt(3)cos(x) = 4sin(x)cos(x). By the "r-alpha" method, the left hand side becomes 2sin(x+60), and you should recognise the right-hand side as 2sin(2x) by the double angle formula. Thus sin(x+60)=sin(2x), so sin(x+60)-sin(x) = 0. Can you now see how to apply the identity and solve the equation from here?

Actually, though, there's no need to use the identity to solve this equation, hence the "or otherwise". I would say the alternative method is easier: If sin(x) = sin(y), we first consider the solutions just within one 360-degree period of the sine function. These principal solutions are x=y and x=180-y, since sin(x) = sin(180-x) is an identity you should know. Now, since the sine graph repeats itself (is periodic) every 360 degrees, we have the complete solution as x = y + 360n or x = 180 - y + 360n, where n is an integer. Here, we apply this with y = x + 60, and again you should be able to proceed yourself from here.

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