103. Найдите значение выражения: а) sin 240°; б) cos (–210°); в) tg 300°; г) sin 330°; д) ctg (–225°); е) sin 315°.

Решение:

1. \( \sin 240^{\circ} = \sin (180^{\circ} + 60^{\circ}) = -\sin 60^{\circ} = -\frac{\sqrt{3}}{2} \).
2. \( \cos (-210^{\circ}) = \cos 210^{\circ} = \cos (180^{\circ} + 30^{\circ}) = -\cos 30^{\circ} = -\frac{\sqrt{3}}{2} \).
3. \( \text{tg} 300^{\circ} = \text{tg} (360^{\circ} - 60^{\circ}) = -\text{tg} 60^{\circ} = -\sqrt{3} \).
4. \( \sin 330^{\circ} = \sin (360^{\circ} - 30^{\circ}) = -\sin 30^{\circ} = -\frac{1}{2} \).
5. \( \text{ctg} (-225^{\circ}) = -\text{ctg} 225^{\circ} = -\text{ctg} (180^{\circ} + 45^{\circ}) = -\text{ctg} 45^{\circ} = -1 \).
6. \( \sin 315^{\circ} = \sin (360^{\circ} - 45^{\circ}) = -\sin 45^{\circ} = -\frac{\sqrt{2}}{2} \).

Ответ: а) \( -\frac{\sqrt{3}}{2} \); б) \( -\frac{\sqrt{3}}{2} \); в) \( -\sqrt{3} \); г) \( -\frac{1}{2} \); д) \( -1 \); е) \( -\frac{\sqrt{2}}{2} \).