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 May 6th, 2014, 12:49 AM #1 Newbie   Joined: May 2014 From: Sydney Posts: 16 Thanks: 0 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?
 May 6th, 2014, 03:20 AM #2 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra $$\cos240^\circ$$ $\displaystyle =\ \cos(180+60)^\circ$ $\displaystyle =\ \cos180^\circ\cos60^\circ - \sin180^\circ\sin60^\circ$ $\displaystyle =\ (-1)\left(\frac12\right)\,-\,(0)\left(\frac{\sqrt3}2\right)$ $\displaystyle =\ -\frac12$
 May 6th, 2014, 07:14 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,624 Thanks: 2077 Using the original reasoning, one gets -sin(30°), which is -1/2, as explained here.

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