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Математика2.6. COS sin(x + \frac{3\pi}{4}) = -\frac{\sqrt{3}}{2};
Ответ:
2.6. sin($$\frac{1}{2}$$x +$$\frac{3\pi}{4}$$) =-$$\frac{\sqrt{3}}{2}$$
$$\frac{1}{2}$$x +$$\frac{3\pi}{4}$$ = arcsin(-$$\frac{\sqrt{3}}{2}$$)
$$\frac{1}{2}$$x +$$\frac{3\pi}{4}$$ =-$$\frac{\pi}{3}$$ + 2$$\pi$$n, n$$\isin$$Z
$$\frac{1}{2}$$x =-$$\frac{\pi}{3}$$ -$$\frac{3\pi}{4}$$ + 2$$\pi$$n, n$$\isin$$Z
$$\frac{1}{2}$$x =-$$\frac{13\pi}{12}$$ + 2$$\pi$$n, n$$\isin$$Z
x =-$$\frac{13\pi}{6}$$ + 4$$\pi$$n, n$$\isin$$Z
$$\frac{1}{2}$$x +$$\frac{3\pi}{4}$$ =$$\pi$$ -(-$$\frac{\pi}{3}$$) + 2$$\pi$$n, n$$\isin$$Z
$$\frac{1}{2}$$x +$$\frac{3\pi}{4}$$ =$$\pi$$ +$$\frac{\pi}{3}$$ + 2$$\pi$$n, n$$\isin$$Z
$$\frac{1}{2}$$x +$$\frac{3\pi}{4}$$ =$$\frac{4\pi}{3}$$ + 2$$\pi$$n, n$$\isin$$Z
$$\frac{1}{2}$$x =$$\frac{4\pi}{3}$$ -$$\frac{3\pi}{4}$$ + 2$$\pi$$n, n$$\isin$$Z
$$\frac{1}{2}$$x =$$\frac{7\pi}{12}$$ + 2$$\pi$$n, n$$\isin$$Z
x =$$\frac{7\pi}{6}$$ + 4$$\pi$$n, n$$\isin$$Z
Ответ: x =-$$\frac{13\pi}{6}$$ + 4$$\pi$$n, x =$$\frac{7\pi}{6}$$ + 4$$\pi$$n, n$$\isin$$Z
Похожие
- 2.1. sin(x - \frac{\pi}{6}) = \frac{1}{2};
- 2.2. cos(x - \frac{\pi}{4}) = -\frac{\sqrt{2}}{2};
- 2.3. sin(x - \frac{5\pi}{6}) = \frac{\sqrt{3}}{2};
- 2.4. sinx+ = -\frac{1}{2};
- 2.5. cos(x - \frac{\pi}{6}) = \frac{1}{2};
- 2.7. sin(2x - \frac{\pi}{6}) = \frac{1}{2};
- 2.8. cos(x + \frac{3\pi}{4}) = -\frac{\sqrt{3}}{2};
- 2.9. sin(x - \frac{2\pi}{3}) = \frac{\sqrt{2}}{2};
- 2.10. cos(x + = -\frac{1}{2};
- 2.11. sin(2x - = -\frac{1}{2};
- 2.12. cos(2x -
