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Chloe's question at Yahoo! Answers involving the angle sum identity for cosine

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MarkFL

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Feb 24, 2012
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Here is the question:

Help with precalculus! Sum or difference formula?

Find the exact value of the given expression using a sum or difference formula.
cos11π/12

A) (sqrt3 - 1)/(2sqrt2)
B) (-sqrt3 + 1)/(2sqrt2)
C) (-sqrt3 - 1)/(2sqrt2)
D) (sqrt3 +1)/(2sqrt2)
Here is a link to the question:

Help with precalculus! Sum or difference formula? - Yahoo! Answers

I have posted a link there to this question so the OP can find my response.
 
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MarkFL

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Feb 24, 2012
13,775
Re: Chloe's question at Yahoo! Questions involving the angle sum identity for cosine

Hello Chloe,

I find it simpler to convert the argument of the cosine function into degrees, to see how best to break it up as a sum or difference:

\(\displaystyle \frac{11\pi}{12}\cdot\frac{180^{\circ}}{\pi}=165^{\circ}=135^{\circ}+30^{\circ}\)

Now, using the angle-sum identity for cosine, we find:

\(\displaystyle \cos\left(135^{\circ}+30^{\circ} \right)=\cos\left(135^{\circ} \right)\cos\left(30^{\circ} \right)-\sin\left(135^{\circ} \right)\sin\left(30^{\circ} \right)=-\frac{1}{\sqrt{2}}\cdot\frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\cdot\frac{1}{2}=-\frac{\sqrt{3}+1}{2\sqrt{2}}\)

This is equivalent to choice C.

To Chloe and any other guests viewing this topic, I invite and encourage you to post other trigonometry problems here in our Trigonometry forum.

Best Regards,

Mark.