Question

Evaluate $\cos 3\mathrm{\pi }$

Answer 1

To evaluate: $\cos 3\mathrm{\pi }$

$\cos 3\mathrm{\pi }$$=\cos (3\times {180}^0)$ $(\mathrm{\pi }={180}^0)$

$=\cos \left({540}^0\right)$

$=\cos ({360}^0+{180}^0)$

$=\cos {180}^0$ $\left[\cos \right({360}^0+\mathrm{\theta })=\mathrm{cos\theta }]$

$=\cos ({90}^0+{90}^0)$

$=-\sin {90}^{\mathrm{o}}$ $\left[\cos \right({90}^0+\mathrm{\theta })=-\mathrm{sin\theta }]$

$=-1$

Hence ,$\cos 3\mathrm{\pi }$$=-1$