6. Вычислите: 1) sin 225°; 2) cos 570°; 3) tg 390°; 4) ctg 765°; 5) sin(-21π/4); 6) cos(31π/6); 7) tg(17π/3); 8) ctg(-19π/4).

Question

Вопрос:

Accepted Answer

1) sin 225° = sin(180° + 45°) = -sin 45° = -√2/2
2) cos 570° = cos(570° - 360°) = cos 210° = cos(180° + 30°) = -cos 30° = -√3/2
3) tg 390° = tg(390° - 360°) = tg 30° = 1/√3 = √3/3
4) ctg 765° = ctg(765° - 2 * 360°) = ctg(45°) = 1
5) sin(-21π/4) = sin(-21π/4 + 6π) = sin(3π/4) = sin(π - π/4) = sin(π/4) = √2/2
6) cos(31π/6) = cos(5π + π/6) = cos(π + π/6) = -cos(π/6) = -√3/2
7) tg(17π/3) = tg(5π + 2π/3) = tg(π + 2π/3) = tg(2π/3) = -√3
8) ctg(-19π/4) = ctg(-19π/4 + 5 * 2π) = ctg(π/4) = 1

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