47. Найдите значения выражений. a) √3 sin 240°; 6) -2√2 sin 405"; д) -3√2 cos 675°; c) 7√3 cos150°; B) 8sin 750°; *) -12cos480°; г) 5√3sin(-540) 3) 13cos(-720) n) 29tg900°; x) 8/3 tg(-240°); 1)18315°: M)-10-31g 600

Ответ:

a) \(\sqrt{3} \sin 240^\circ = \sqrt{3} \sin (180^\circ + 60^\circ) = \sqrt{3} (-\sin 60^\circ) = \sqrt{3} \cdot\left(-\frac{\sqrt{3}}{2}\right) = -\frac{3}{2} = -1.5\)

б) \(-2\sqrt{2} \sin 405^\circ = -2\sqrt{2} \sin (360^\circ + 45^\circ) = -2\sqrt{2} \sin 45^\circ = -2\sqrt{2} \cdot \frac{\sqrt{2}}{2} = -2\)

в) \(8 \sin 750^\circ = 8 \sin (2 \cdot 360^\circ + 30^\circ) = 8 \sin 30^\circ = 8 \cdot \frac{1}{2} = 4\)

г) \(5 \sqrt{3} \sin (-540^\circ) = 5 \sqrt{3} \sin (-360^\circ - 180^\circ) = 5 \sqrt{3} \sin (-180^\circ) = 5 \sqrt{3} \cdot 0 = 0\)

д) \(-3\sqrt{2} \cos 675^\circ = -3\sqrt{2} \cos (2 \cdot 360^\circ - 45^\circ) = -3\sqrt{2} \cos (-45^\circ) = -3\sqrt{2} \cdot \frac{\sqrt{2}}{2} = -3\)

e) \(7\sqrt{3} \cos 150^\circ = 7\sqrt{3} \cos (180^\circ - 30^\circ) = 7\sqrt{3} (-\cos 30^\circ) = 7\sqrt{3} \cdot \left(-\frac{\sqrt{3}}{2}\right) = -\frac{21}{2} = -10.5\)

ж) \(-12 \cos 480^\circ = -12 \cos (360^\circ + 120^\circ) = -12 \cos 120^\circ = -12 \cdot \left(-\frac{1}{2}\right) = 6\)

з) \(13 \cos (-720^\circ) = 13 \cos (-2 \cdot 360^\circ) = 13 \cos 0^\circ = 13 \cdot 1 = 13\)

и) \(29 \operatorname{tg} 900^\circ = 29 \operatorname{tg} (2 \cdot 360^\circ + 180^\circ) = 29 \operatorname{tg} 180^\circ = 29 \cdot 0 = 0\)

к) \(8 \sqrt{3} \operatorname{tg} (-240^\circ) = 8 \sqrt{3} \operatorname{tg} (-180^\circ - 60^\circ) = 8 \sqrt{3} \operatorname{tg} (-60^\circ) = 8 \sqrt{3} \cdot (-\sqrt{3}) = -24\)

л) \(\frac{3}{2} \operatorname{tg} 315^\circ = \frac{3}{2} \operatorname{tg} (360^\circ - 45^\circ) = \frac{3}{2} \operatorname{tg} (-45^\circ) = \frac{3}{2} \cdot (-1) = -\frac{3}{2} = -1.5\)

м) \(-10\sqrt{3} \operatorname{tg} 600^\circ = -10\sqrt{3} \operatorname{tg} (360^\circ + 240^\circ) = -10\sqrt{3} \operatorname{tg} 240^\circ = -10\sqrt{3} \operatorname{tg} (180^\circ + 60^\circ) = -10\sqrt{3} \cdot \sqrt{3} = -30\)

Ответ: a) -1.5; б) -2; в) 4; г) 0; д) -3; e) -10.5; ж) 6; з) 13; и) 0; к) -24; л) -1.5; м) -30