Задание 16.7

Question

16.7. $^{\circ}$ Решите уравнение:
1) $\operatorname{tg} 2 x=1$
2) $\operatorname{tg} \frac{x}{3}=\frac{1}{3}$
3) $\operatorname{tg}\left(-\frac{7 x}{4}\right)=\sqrt{3}$

Gimli · Accepted Answer

Gimli · Answer

$16.7$
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1)$\operatorname{tg} 2 x=1$
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$2 x=\operatorname{arctg} 1+\pi n$
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$2 x=\frac{\pi}{4}+\pi n$
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$x=\frac{\pi}{8}+\frac{\pi}{2} n, n \in z$
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$2) \operatorname{tg} \frac{x}{3}=\frac{1}{3}$
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$\frac{x}{3}=\operatorname{arctg} \frac{1}{3}+\pi n$
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$x=3 \cdot \operatorname{arctg} \frac{1}{3}+3 \pi n, n \in Z$
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3) $\operatorname{tg}\left(-\frac{7 x}{4}ight)=\sqrt{3}$
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$\frac{-7 x}{4}=\operatorname{arctg} \sqrt{3}+\pi n$
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$-7 x=4 \cdot \operatorname{arctg} \sqrt{3}+4 \pi n$
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$x=-\frac{4}{7} \operatorname{arctg} \sqrt{3}+\frac{4}{7} \pi n$
$n \in z .$

Задание 16.7

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Задание 16.7

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