Задание 4. Вычислите: 1) cos 180° − sin 0°; 2) sin 270° + cos 90° · tg 120° − sin 210°; 3) (√2/2) · cos 45° − √2 sin 45° + (tg 30° − ctg 60°)/√3; 4) sin(π/3) cos(π/6) + tg(π/4) · ctg(π/4); 5) (cos 90° + sin 810°)/(ctg(5π/2) − tg(9π/4)).

Question

Вопрос:

Accepted Answer

\(\cos180^\circ-\sin0^\circ=-1-0=-1\).
\(\sin270^\circ+\cos90^\circ\cdot\operatorname{tg}120^\circ-\sin210^\circ=-1+0\cdot(-\sqrt3)-(-\frac12)=-\frac12\).
\[\frac{\sqrt2}{2}\cdot\cos45^\circ-\sqrt2\sin45^\circ+\frac{\operatorname{tg}30^\circ-\operatorname{ctg}60^\circ}{\sqrt3}=\frac12-1+\frac{\frac1{\sqrt3}-\frac1{\sqrt3}}{\sqrt3}=-\frac12.\]
\[\sin\frac\pi3\cdot\cos\frac\pi6+\operatorname{tg}\frac\pi4\cdot\operatorname{ctg}\frac\pi4=\frac{\sqrt3}{2}\cdot\frac{\sqrt3}{2}+1\cdot1=\frac34+1=\frac74.\]
\[\frac{\cos90^\circ+\sin810^\circ}{\operatorname{ctg}\frac{5\pi}{2}-\operatorname{tg}\frac{9\pi}{4}}=\frac{0+1}{0-1}=-1.\]

Ответ: 1) −1; 2) −1/2; 3) −1/2; 4) 7/4; 5) −1.