Further trig (1 Viewer)

Saturn WY15 · Jul 28, 2012

Cos5x+cosx-cos3x=0 domain -pie<x< pie

SpiralFlex · Jul 28, 2012

$\cos 5x+\cos x - \cos 3x=0$

$By applying sums to product$

$\cos 3x \cos 2x - \cos 3x =0$

$\cos 3x(2\cos 2x - 1)=0$

$You didn't state a domain so just solve it for the domain.$

SunnyScience · Jul 28, 2012

SpiralFlex said:
$\cos 5x+\cos x - \cos 3x=0$

$By applying sums to product$

$\cos 3x \cos 2x - \cos 3x =0$

$\cos 3x(\cos 2x - 1)=0$

$You didn't state a domain so just solve it for the domain.$

How on Earth did you get this?

SpiralFlex · Jul 28, 2012

$First we have the prove this identity.$

$\cos (\alpha+\beta) + \cos (\alpha-\beta) = 2\cos \alpha \cos \beta$

$LHS = \cos \alpha \cos \beta -\sin \alpha \sin \beta + \cos \alpha \cos \beta +\sin \alpha \sin \beta$

$=2\cos \alpha \cos \beta$

$=RHS$

$The reason why I did this was that if you apply the form on the first two expressions, you will see that you get a cosine 3x out. Which is equivalent to the third term. Then you notice the right hand side is zero. So factorisation can be applicable to solve for x in both cases.$

Sy123 · Jul 28, 2012

$\cos (3x+2x) + \cos(3x-2x) - \cos3x=0 \\ \cos 3x \cos 2x - \sin 3x \sin 2x +\cos 3x \cos 2x + \sin 3x \sin 2x -\cos 3x =0 \\ \\ 2\cos 3x \cos 2x -\cos 3x =0 \\ \\ \cos 3x (2\cos 2x -1)=0$

I generally like to prove the identity first though, but its a handy method to do, unless you want to derive cos5x into cos x form

EDIT: Beaten.

SunnyScience · Jul 28, 2012

As a 3U student - are we meant to know this off the top of our head? O_O

SpiralFlex · Jul 28, 2012

No it's not in syllabus but good to know and they get you to prove the result anyway

deswa1 · Jul 28, 2012

SpiralFlex said:
No it's not in syllabus but good to know and they get you to prove the result anyway

Yeah this. Its not even in the 4U course but it can be so useful in solving problems + its not that hard to remember/derive anyway

RealiseNothing · Jul 28, 2012

SpiralFlex said:
$\cos 5x+\cos x - \cos 3x=0$

$By applying sums to product$

$\cos 3x \cos 2x - \cos 3x =0$

$\cos 3x(2\cos 2x - 1)=0$

$You didn't state a domain so just solve it for the domain.$

Check your 3rd line.

bleakarcher · Jul 28, 2012

RealiseNothing said:
Check your 3rd line.

He just screwed up in the latex in the 2nd line, it should be 2cos(3x)cos(2x)-cos(3x)=0

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Further trig (1 Viewer)

Saturn WY15

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SpiralFlex

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SunnyScience

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SpiralFlex

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Sy123

This too shall pass

SunnyScience

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SpiralFlex

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deswa1

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RealiseNothing

what is that?It is Cowpea

bleakarcher

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