№ 10 ВПР 1 Геометрія = № 10 ВПТ 1 Математика
Обчисліть:
1) $\sin 120^{\circ}\cdot\text{tg }120^{\circ}$
2) $\cos 180^{\circ}+sin90^{\circ}$
3) $\cos 120^{\circ}+sin30^{\circ}$
4) $\cos 135^{\circ}\cdot sin135^{\circ}$
Розв’язок:
1) $\sin 120^{\circ}\cdot\text{tg }120^{\circ}=$
$=sin(180^{\circ}-60^{\circ})\cdot\text{tg}(180^{\circ}-60^{\circ})=$
$=sin60^{\circ}\cdot(-\text{tg }60^{\circ})=$
$=\frac{\sqrt{3}}{2}\cdot(-\sqrt{3})=-\frac{3}{2}$
2) $\cos 180^{\circ}+sin90^{\circ}=-1+1=0$
3) $\cos 120^{\circ}+\sin 30^{\circ}=$
$=-cos60^{\circ}+sin30^{\circ}=$
$=-\frac{1}{2}+\frac{1}{2}=0$
4) $\cos 135^{\circ}\cdot\sin 135^{\circ}=$
$=-cos45^{\circ}\cdot sin45^{\circ}=$
$=-\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{2}}{2}=-\frac{2}{4}=-\frac{1}{2}$