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May 6th, 2014, 12:49 AM   #1
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trigonometry surd

What is the exact value of cos240?
Shouldn't it be cos30(being closer to 270)
Thus √3/2?
However the answer says -1/2
Why is that?
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May 6th, 2014, 03:20 AM   #2
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$$\cos240^\circ$$
$\displaystyle =\ \cos(180+60)^\circ$

$\displaystyle =\ \cos180^\circ\cos60^\circ - \sin180^\circ\sin60^\circ$

$\displaystyle =\ (-1)\left(\frac12\right)\,-\,(0)\left(\frac{\sqrt3}2\right)$

$\displaystyle =\ -\frac12$
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May 6th, 2014, 07:14 AM   #3
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Using the original reasoning, one gets -sin(30°), which is -1/2, as explained here.
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