1003086102 Level: BHow many solutions does the equation \( \mathrm{cotg}\left(2x - \frac{\pi}4\right) = \frac1{\sqrt3} \) have in the interval \( [0;2\pi] \)?\( 4 \)\( 8 \)\( 2 \)\( 0 \)
1003086101 Level: BWhich of the following equations has exactly four solutions in the interval \( [0;\pi] \)?\( \mathrm{tg}\,4x = 2 \)\( \mathrm{tg}\,2x = 4 \)\( \mathrm{tg}\,\frac x4 = 2 \)\( \mathrm{tg}\,\frac x4 = 4 \)
1003085810 Level: BLet \( x\in\left(\frac{\pi}2;\pi\right] \). Which of the following statements is true?\( \sin x \geq \mathrm{tg}\,x \)\( \sin x > \mathrm{tg}\,x \)\( \sin x < \mathrm{tg}x \)\( \sin x \leq \mathrm{tg}\,x \)
1003085809 Level: BWhich of the following inequalities has no solution for \( x\in\mathbb{R} \)?\( 99\cos x >100 \)\( \cos^2x -\sin^2x \geq 1 \)\( \sin|x| < 0 \)\( \sin 2x \leq 2 \)
1003085808 Level: BWhich of the following inequalities has no solutions for \( x\in\mathbb{R} \)?\( \cos^2x -\sin^2x > 1 \)\( 100\sin x > 1 \)\( \sin x \cdot \cos x \geq \frac12 \)\( |\sin x| \geq 1 \)
1003085807 Level: BFor which \( x\in\left(-\frac{\pi}2;\ \frac{\pi}2\right) \) is the inequality \( \mathrm{tg}\,3x < -1 \) true?\( x\in\left(-\frac{\pi}2;-\frac{5\pi}{12}\right)\cup\left(-\frac{\pi}6;-\frac{\pi}{12}\right)\cup\left(\frac{\pi}6;\frac{\pi}4\right) \)\( x\in\left(-\frac{\pi}6;-\frac{\pi}{12}\right)\cup\left(\frac{\pi}6;\frac{\pi}4\right) \)\( x\in\left(-\frac{\pi}2;-\frac{5\pi}{12}\right)\cup\left(-\frac{\pi}6; - \frac{\pi}{12}\right) \)\( x\in\left(-\frac{\pi}6; -\frac{\pi}{12}\right)\cup\left(\frac{\pi}{12};\frac{\pi}6\right)\cup\left(\frac{\pi}6;\frac{\pi}4\right) \)
1003085806 Level: BThe solution set of the inequality \( \mathrm{tg}\,x > 1 \) for \( 0 \leq x \leq \pi \) is the interval:\( \left(\frac{\pi}4;\frac{\pi}2 \right) \)\( \left(0;\frac{\pi}4 \right) \)\( \left(0;\frac{\pi}2 \right) \)\( \left(\frac{\pi}2;\pi \right) \)
1003085805 Level: BThe solution set of the inequality \( 2\sin x \leq 3 \) for \( x\in\mathbb{R} \) is:\( \mathbb{R} \)\( \emptyset \)\( [0;\pi] \)\( [ 0;2\pi ] \)
1003085804 Level: BThe solution set of the inequality \( \sin x > \cos x \) for \( x\in\mathbb{R} \) is:\( \bigcup\limits_{k\in\mathbb{Z}}\left(\frac{\pi}4+2k\pi;\ \frac{5\pi}4+2k\pi\right) \)\( \bigcup\limits_{k\in\mathbb{Z}}\left(\frac{\pi}4+k\pi;\ \frac{5\pi}4+k\pi \right) \)\( \bigcup\limits_{k\in\mathbb{Z}}\left(\frac{\pi}3+2k\pi;\ \frac{5\pi}3+2k\pi\right) \)\( \bigcup\limits_{k\in\mathbb{Z}}\left(\frac{\pi}3+k\pi;\ \frac{5\pi}3+k\pi \right) \)
1003085803 Level: BThe solution set of the inequality \( \mathrm{cotg}\,x \leq \sqrt3 \) for \( x\in\mathbb{R} \) is:\( \bigcup\limits_{k\in\mathbb{Z}}\left[\frac{\pi}6+k\pi;\ (k+1)\pi\right) \)\( \bigcup\limits_{k\in\mathbb{Z}}\left[\frac{\pi}6+2k\pi;\ \frac{\pi}2+2k\pi\right] \)\( \bigcup\limits_{k\in\mathbb{Z}}\left[\frac{\pi}3+k\pi;\ \frac{\pi}2+k\pi\right] \)\( \bigcup\limits_{k\in\mathbb{Z}}\left[\frac{\pi}3+2k\pi;\ \frac{\pi}2+2k\pi\right] \)