Question

Cum se rezolva aceast exercitiu? cos(2008π/3)

Answer 1

$\cos( \frac{2008\pi}{3} ) \\ \\ \cos( \frac{2004\pi + 4\pi}{3} ) \\ \\\cos( 668\pi + \frac{4\pi}{3} ) \\ \\ \cos(2 \times 334\pi + \frac{3\pi + \pi}{3} ) \\ \\ \cos(\pi + \frac{\pi}{3} ) \\ \\ - \cos( \frac{\pi}{3} ) = - \frac{1}{2}$

Answer 2

[tex]\cos \left(2008\cdot \frac{\pi }{3}\right) \\ \\ \cos \left(\frac{2008\pi }{3}\right) \\ \\ \cos \left(\frac{2008\pi }{3}\right)=\cos \left(\frac{2004+4}{3}\pi \right)=\cos \left(\left(\frac{2004}{3}+\frac{4}{3}\right)\pi \right)=\cos \left(2\pi \cdot \:334+\frac{4}{3}\pi \right) \\ \\ \cos \left(2\pi \cdot \:334+\frac{4}{3}\pi \right)=\cos \left(\frac{4}{3}\pi \right) =\ \textgreater \ =\cos \left(\pi +\frac{\pi }{3}\right)[/tex][tex]=\cos \left(\pi \right)\cos \left(\frac{\pi }{3}\right)-\sin \left(\pi \right)\sin \left(\frac{\pi }{3}\right) \\ \\ \cos \left(\pi \right)=\left(-1\right) \\ \\ \sin \left(\pi \right)=0 \\ \\ \cos \left(\frac{\pi }{3}\right)=\frac{1}{2} \\ \\ \sin \left(\frac{\pi }{3}\right)=\frac{\sqrt{3}}{2} \\ \\ =\left(-1\right)\frac{1}{2}-0\cdot \frac{\sqrt{3}}{2} \\ \\ =-\frac{1}{2} \\ \\ [/tex]