Question

Вычислите cos 105 градусов, sin 300 градусов и tg 41Пи/4

Answer 1

$sin300^circ =sin(360^circ -60^circ )=-sin60^circ =-frac{sqrt3}{2}\\tgfrac{41pi}{4}=tg(10pi +frac{pi}{4})=tgfrac{pi}{4}=1\\cos105^circ =cos(90^circ +15^circ)=-sin15^circ=-sin(45^circ-30^circ)=\\=-sin45cdot cos30+cos45cdot sin30=-frac{sqrt2}{2}cdot frac{sqrt3}{2}+frac{sqrt2}{2}cdot frac{1}{2}=\\=frac{sqrt2(1-sqrt3)}{4}=frac{sqrt2-sqrt6}{4}$