Question

Вычислить,используя формулы : sin 225 градусов+cos 330 градусов+ ctg 510 градусов

Answer 1

$\sin225^\circ+\cos330^\circ+{\rm ctg}510^\circ=\sin(180^\circ+45^\circ)+\cos(360^\circ-30^\circ)+\\+{\rm ctg}(540^\circ-30^\circ)=-\sin45^\circ+\cos30^\circ-{\rm ctg}30^\circ=\\=-\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{3}}{2}-\sqrt{3}=-\dfrac{\sqrt{2}+\sqrt{3}}{2}$

Answer 2

   sin 225° + cos 330° + ctg 510° =

= sin (180° + 45°) + cos (270° + 60°) + ctg (360° + 90° + 60°) =

= - sin 45° + sin 60° - tg 60° =

$= -\dfrac{\sqrt{2}}{2} + \dfrac{\sqrt{3}}{2}-\sqrt{3}= -\dfrac{\sqrt{2}}{2} - \dfrac{\sqrt{3}}{2}= -\dfrac{\sqrt{2}+\sqrt{3}}{2}=\\ \\ \\ \boldsymbol{=-0,5(\sqrt{2}+\sqrt{3})}$

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Использованы формулы

sin (180° + α) = - sin α

cos (270° + α) = cos α

ctg (90° + α) = - tg α

ctg (360° + α) = ctg α