Quiz about Найпростіші тригонометричні рівняння

Question 1

arcsin (1) =

Accepted Answer

$$\frac{\pi}{2}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$\pi$$

Question 2

$$ar\operatorname{ctg}\left(-1\right)=$$

Accepted Answer

$$-\frac{\pi}{4}$$

Answer

$$\frac{\pi}{2}$$

Answer

$$\frac{\pi}{4}$$

Answer

$$\frac{3\pi}{4}$$

Question 3

$$\arccos\left(\frac{1}{2}\right)=$$

Accepted Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{\pi}{2}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{\pi}{4}$$

Question 4

$$\operatorname{arcctg}\ \left(-\frac{\sqrt{3}}{3}\right)=$$

Accepted Answer

$$\frac{2\pi}{3}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{5\pi}{6}$$

Answer

$$-\frac{\pi}{6}$$

Question 5

$$tg\left(\frac{x}{6}\right)=\sqrt{3}$$ , $$x=$$

Accepted Answer

$$2\pi+6\pi k$$

Answer

$$\frac{\pi}{3}+\pi k$$

Answer

$$\frac{\pi}{3}+2\pi k$$

Answer

$$3\pi+6\pi k$$

Answer

$$2\pi+12\pi k$$

Question 6

$$\sin\left(\frac{\pi}{9}x\right)=\frac{1}{2}$$ , $$x=$$

Accepted Answer

$$\left(-1\right)^k\ \frac{3}{2}+9k$$

Answer

$$\left(-1\right)^k\ \frac{3}{2}+9\pi k$$

Answer

$$\left(-1\right)^k\ \frac{2}{3}+9k$$

Answer

$$\pm\frac{2}{3}+9k$$

Question 7

$$\cos\ \left(x\right)=-\frac{\sqrt{3}}{2}$$ , $$x=$$

Accepted Answer

$$\pm\frac{5\pi}{6}+2\pi k$$

Answer

$$\pm\frac{\pi}{6}+2\pi k$$

Answer

$$\pi\pm\frac{\pi}{6}+2\pi k$$

Answer

$$\pm\frac{7\pi}{6}+2\pi k$$

Question 8

$$\cos^2x+2\cos x-3=0$$ , $$x=$$

Accepted Answer

$$2\pi k$$

Answer

$$2\pi k\ та\ \pm\arcsin\left(-3\right)+2\pi k$$

Answer

$$2\pi k\ та\ \pm\arccos\left(-3\right)+2\pi k$$

Answer

$$2\pi k\ та\ \pm\arccos\left(3\right)+2\pi k$$

Answer

$$\pi k$$

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