Free Printable Тригонометрия

1.

a)

$\frac{69}{128}$

b)

$\frac{79}{128}$

c)

$\frac{59}{128}$

d)

$\frac{79}{127}$

2.

a)

$\sqrt{3,5}$

b)

$\sqrt{3}$

c)

$\sqrt{2}$

d)

$\sqrt{0,96}$

3.

a)

$\frac{65}{16}$

b)

$\frac{13}{65}$

c)

$\frac{65}{13}$

d)

$\frac{16}{65}$

4.

a)

$tg^3a$

b)

$tg^2a$

c)

$tg3a$

d)

tg2a

5.

a)

$\left(\frac{7}{6}+k;\frac{5}{6}+k\right)\left(\frac{1}{6}+k;-\frac{1}{6}+k\right)$

b)

$\left(\frac{5}{6}+k;\frac{1}{6}+k\right)\left(\frac{7}{6}+k;-\frac{7}{6}+k\right)$

c)

$\left(\frac{7}{6}+k:\frac{1}{6}+k\right)\left(\frac{5}{6}+k;-\frac{1}{6}+k\right)$

d)

$\left(\frac{-7}{6}+k;\frac{1}{6}+k\right)\left(\frac{5}{6}+k;-\frac{1}{6}+k\right)$

6.

a)

$\left(-\frac{\pi}{6}+2\pi n;\frac{\pi}{6}+2\pi n\right)$

b)

$\left(\frac{\pi}{3}+2\pi n;\frac{5\pi}{3}+2\pi n\right)$

c)

$\left(-\frac{\pi}{6}+2\pi n;\frac{\pi}{3}+2\pi n\right)$

d)

$\left(\frac{\pi}{6}+2\pi n;\frac{5\pi}{6}+2\pi n\right)$

7.

a)

$\left[-\frac{\pi}{18}+\pi k;\frac{\pi}{4}\pi\kappa\right],k\ \in Z$

b)

$\left[-\frac{\pi}{12}+\pi k;\frac{\pi}{4}\pi\kappa\right],k\ \in Z$

c)

$\left[-\frac{\pi}{12}+\pi k;\frac{\pi}{5}\pi\kappa\right],k\ \in Z$

d)

$\left[\frac{\pi}{12}+\pi k;\frac{\pi}{4}\pi\kappa\right],k\ \in Z$

8.

a)

$\left(-\frac{\pi}{4}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2};\frac{\pi}{4}+\frac{\pi k}{2}\right)\ k\in Z$

b)

$\left(-\frac{\pi}{4}+\frac{\pi k}{2};\ \frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2};\frac{\pi}{4}+\frac{\pi k}{2}\right)\ k\in Z$

c)

$\left(\frac{\pi}{4}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2};\frac{\pi}{4}+\frac{\pi k}{2}\right)\ k\in Z$

d)

$\left(-\frac{\pi}{4}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{4}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2};\frac{\pi}{4}+\frac{\pi k}{2}\right)\ k\in Z$

9.

a)

$\left(-\frac{\pi}{3}+\pi n;\frac{\pi}{3}+\pi n\right)$

b)

$\left(\frac{\pi}{3}+\pi n;\frac{2\pi}{3}+\pi n\right)$

c)

$\left(\frac{\pi}{3}+\pi n;\frac{3\pi}{2}+\pi n\right)$

d)

$\left(-\frac{\pi}{2}+\pi n;\frac{\pi}{6}+\pi n\right)$

10.

a)

$\frac{3\pi}{16}+\frac{\pi k}{2};\frac{5\pi}{8}+\pi k.k\in Z$

b)

$\frac{3\pi}{4}+\frac{\pi k}{2};\frac{5\pi}{8}+\pi k.k\in Z$

c)

$\frac{\pi}{16}+\frac{\pi k}{2};\frac{5\pi}{8}+\pi k.k\in Z$

d)

$\frac{3\pi}{2}+\frac{\pi k}{4};\frac{5\pi}{8}+\pi k.k\in Z$

11.

a)

$\left[\frac{\pi}{8}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right)$

b)

$\left[\frac{\pi}{4}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right)$

c)

$\left[\frac{\pi}{6}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right)$

d)

$\left[\frac{\pi}{3}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{4}\right)$

12.

a)

$\left[\frac{1}{3}\arccos\ \frac{2}{3}+\pi k;\pi-\frac{1}{2}\arccos\ \frac{2}{3}+\pi k\right]\ k\in Z$

b)

$\left[\frac{1}{2}\arccos\ \frac{2}{3}+\pi k;\pi-\frac{1}{2}\arccos\ \frac{2}{3}+\pi k\right]\ k\in Z$

c)

$\left[\frac{1}{3}\arccos\ \frac{2}{3}+\pi k;\pi+\frac{1}{2}\arccos\ \frac{2}{3}+\pi k\right]\ k\in Z$

d)

$\left[\frac{1}{2}\arccos\ \frac{2}{3}+\pi k;\pi-\frac{1}{2}\arccos\ \frac{2}{3}+\pi k\right]\ k\in Z$

13.

a)

$\left[-\frac{5\pi}{6}+2\pi k;-\arccos\ \frac{2}{3}+2\pi k\right)\cup\left(\arccos\ \frac{2}{3}+2\pi k;\frac{5\pi}{6}+2\pi k\right]\ k\in Z$

b)

$\left[-\frac{5\pi}{6}+2\pi k;\ \arccos\ \frac{2}{3}+2\pi k\right)\cup\left(\arccos\ \frac{2}{3}+2\pi k;\frac{5\pi}{6}+2\pi k\right]\ k\in Z$

c)

$\left[\frac{7\pi}{6}+2\pi k;-\arccos\ \frac{2}{3}+2\pi k\right)\cup\left(\arccos\ \frac{2}{3}+2\pi k;\frac{7\pi}{6}+2\pi k\right]\ k\in Z$

d)

$\left[-\frac{\pi}{6}+2\pi k;-\arccos\ \frac{2}{3}+2\pi k\right)\cup\left(\arccos\ \frac{2}{3}+2\pi k;\frac{\pi}{6}+2\pi k\right]\ k\in Z$

14.

a)

$3ar\operatorname{ctg}\ \frac{1}{3}+3\pi k,3ar\operatorname{ctg}2+3\pi k,\ k\in Z$

b)

$3ar\operatorname{ctg}\ \frac{1}{2}+3\pi k,2ar\operatorname{ctg}2+3\pi k,\ k\in Z$

c)

$ar\operatorname{ctg}\ \frac{1}{3}+3\pi k,\ ar\operatorname{ctg}2+3\pi k,\ k\in Z$

d)

$3ar\operatorname{ctg}\ \frac{1}{4}+3\pi k,3ar\operatorname{ctg}2+3\pi k,\ k\in Z$

15.

a)

$\frac{5\pi}{12}+\frac{1}{2}+\pi k,k\in Z$

b)

$\frac{5\pi}{12}-\frac{1}{2}+\pi k,k\in Z$

c)

$\frac{7\pi}{12}+\frac{1}{2}+\pi k,k\in Z$

d)

$\frac{5\pi}{18}+\frac{1}{2}+\pi k,k\in Z$

16.

a)

$\pm\frac{2\pi}{3}+2\pi k,k\in Z$

b)

$\pm\frac{\pi}{3}+2\pi k,k\in Z$

c)

$\pm\frac{\pi}{4}+2\pi k,k\in Z$

d)

$\pm\frac{3\pi}{2}+2\pi k,k\in Z$

17.

a)

$\left(-\frac{\pi}{4}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\ \cup\ \left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\div\frac{\pi}{4}-\frac{\pi k}{2}\right)\cup\ y=\cos^2\left(2x-\frac{\pi}{3}\right)$

b)

$\left(-\frac{\pi}{4}+\frac{\pi k}{4};-\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{4}\right)\ \cup\ \left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\div\frac{\pi}{4}-\frac{\pi k}{2}\right)\cup\ y=\cos^2\left(2x-\frac{\pi}{3}\right)$

c)

$\left(-\frac{\pi}{6}+\frac{\pi k}{2};-\frac{1}{4}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\ \cup\ \left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\div\frac{\pi}{4}-\frac{\pi k}{2}\right)\cup\ y=\cos^2\left(2x-\frac{\pi}{3}\right)$

d)

$\left(-\frac{\pi}{3}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{3}\right)\ \cup\ \left(\frac{1}{2}ar\operatorname{ctg}\ \frac{1}{\sqrt{2}}+\frac{\pi k}{2}\div\frac{\pi}{4}-\frac{\pi k}{2}\right)\cup\ y=\cos^2\left(2x-\frac{\pi}{3}\right)$

18.

a)

$x=\pm\frac{\pi}{6}+\pi n$

b)

$x=\pm\frac{\pi}{2}+\pi n$

c)

$x=\pm\frac{\pi}{4}+\pi n$

d)

$x=\pm\frac{2\pi}{3}+\pi n$

19.

Ең кіші оң периодын табыңыз

a)

$12\pi$

b)

$6\pi$

c)

$-12\pi$

d)

$-6\pi$

20.

a)

$\left(-\frac{\pi}{3}+\pi n;\frac{5\pi}{12}+\pi n\right)$

b)

$\left(\frac{\pi}{3}+\pi n;\frac{5\pi}{12}+\pi n\right)$

c)

$\left(\frac{\pi}{3}+\pi n;\frac{7\pi}{12}+\pi n\right)$

d)

$\left(-\frac{\pi}{6}+\pi n;\frac{5\pi}{12}+\pi n\right)$

21.

a)

$\frac{\pi}{4}+\pi n$

b)

$\frac{\pi}{2}+\pi n$

c)

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

d)

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

22.

a)

$\left(\pi+2\pi k;2\pi+2\pi k\right)$

b)

$\left(\pi+2\pi k;3\pi+2\pi k\right)$

c)

$\left(\frac{\pi}{2}+2\pi k;\pi+2\pi k\right)$

d)

$\left(\frac{\pi}{4}+2\pi k;2\pi+2\pi k\right)$

23.

a)

$\frac{\pi}{2}+\pi k;\frac{\pi}{4}+\pi k$

b)

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

c)

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

d)

$-\frac{\pi}{2}+\pi k;\frac{\pi}{2}+\pi k$

24.

a)

$\left(-\infty,+\infty\right)$

b)

$\left(-\infty1,5\right)$

c)

$\left(-\infty,8\right)$

d)

$\left(5,+\infty\right)$

25.

a)

$\left(-1\right)^{k\ }\cdot\frac{2\pi}{3}-\frac{2\pi}{3}+2\pi k,\ k\in Z$

b)

$\left(-1\right)^{k\ }\cdot\frac{3\pi}{2}-\frac{\pi}{6}+2\pi k,\ k\in Z$

c)

$\left(-1\right)^{k\ }\cdot\frac{\pi}{3}-\frac{\pi}{3}+2\pi k,\ k\in Z$

d)

$\left(-1\right)^{k\ }\cdot\frac{\pi}{6}-\frac{\pi}{6}+2\pi k,\ k\in Z$

26.

a)

$\pm\frac{3\pi}{2}+2\pi k,\ k\in Z$

b)

$\pm\frac{2\pi}{3}+\pi k,\ k\in Z$

c)

$\pm\frac{2\pi}{3}+2\pi k,\ k\in Z$

d)

$\pm\frac{\pi}{3}+2\pi k,\ k\in Z$

27.

$\sin^2\ 3x\ =\ 3\cos^2\ 3x$

a)

$\frac{\pi}{6}\left(3n\pm1\right)$

b)

$\frac{\pi}{9}\left(3n\pm1\right)$

c)

$\frac{\pi}{6}\left(2n\pm1\right)$

d)

$\frac{\pi}{9}\left(2n\pm1\right)$

28.

$\sin^2x\ +\ \frac{1}{2}\sin2x\ =\ 1$

a)

$\frac{\pi}{2}+2\pi k;\ \frac{\pi}{4}+2\pi k$

b)

$\frac{\pi}{2}+\pi k;\ \frac{\pi}{4}+\pi n$

c)

$\frac{\pi}{3}+\pi k;\ \frac{\pi}{6}+\pi n$

d)

$-\frac{\pi}{2}+\pi k;\ \frac{\pi}{4}+\pi n$

29.

$3\sin^2\ \frac{x}{2}\ +\ 2\cos^2\ \frac{x}{3}-3.5\sin\ \frac{2x}{3}\ =\ 0$

a)

$3acrtg\ \frac{1}{2}+2\pi k,\ 3ar\operatorname{ctg}2+2\pi k,\ k\in Z$

b)

$2acrtg\ \frac{1}{3}+3\pi k,\ 2ar\operatorname{ctg}2+3\pi k,\ k\in Z$

c)

$acrtg\ \frac{1}{2}+3\pi k,\ ar\operatorname{ctg}2+3\pi k,\ k\in Z$

d)

$3acrtg\ \frac{1}{3}+3\pi k,\ 3ar\operatorname{ctg}2+3\pi k,\ k\in Z$

30.

cos2x = 3 + 7cosx

a)

$\pm\frac{2\pi}{3}+\pi k,\ k\in Z$

b)

$\pm\frac{\pi}{3}+2\pi k,\ k\in Z$

c)

$\pm\frac{2\pi}{3}+2\pi k,\ k\in Z$

d)

$2\pi k,\ k\in Z$

31.

$\sin^2x\ +\ \frac{1}{2}\sin2x=1$

a)

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

b)

$\frac{\pi}{2}+\pi k;\ \frac{\pi}{4}\pi k;$

c)

$-\frac{\pi}{2}+\pi k;\ \frac{\pi}{4}\pi k;$

d)

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

32.

$\sin x-\cos x=\sqrt{2}\cos3x$

a)

$\frac{3\pi}{16}+\frac{\pi k}{2};\frac{5\pi}{8}+\pi k,\ k\in Z$

b)

$\frac{\pi}{16}+\pi k;\frac{3\pi}{8}+\pi k,\ k\in Z$

c)

$\frac{3\pi}{8}+\pi k\cdot\frac{5\pi}{4}+\pi k,\ k\in Z$

d)

$\frac{3\pi}{16}+\frac{\pi k}{2}\cdot\frac{5\pi}{8},\ k\in Z$

33.

$2\sin\left(\frac{x}{2}+\frac{\pi}{3}\right)-\sqrt{3}=0$

a)

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

b)

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

c)

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

d)

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

34.

$tg^2x\ -\ 3tgx+4=3\operatorname{ctg}x-\operatorname{ctg}^2x$

a)

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

b)

$\frac{\pi}{4}+2\pi k$

c)

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

d)

$\frac{\pi}{4}+\pi k$

35.

$9\cos\left(1-2x\right)-\sqrt{27}\sin\left(2x-1\right)=-6\sqrt{3}$

a)

$\frac{5\pi}{12}+2+\pi k,\ k\in Z$

b)

$\frac{5\pi}{12}+\frac{1}{2}+\pi k,\ k\in Z$

c)

$\frac{10\pi}{2}+\frac{1}{2}+\pi k,\ k\in Z$

d)

$\frac{5\pi}{12}+\frac{1}{4}+2\pi k,\ k\in Z$

36.

$\cos2x\ =\ 3+7\cos x$

a)

$\pm\frac{\pi}{6}+\pi k,\ k\in Z$

b)

$\pm\frac{2\pi}{3}-2\pi k,\ k\in Z$

c)

$\pm\frac{2\pi}{3}+2\pi k,\ k\in Z$

d)

$\pm\frac{\pi}{4}+2\pi k,\ k\in Z$

37.

$\sin^2x+\frac{1}{2}\sin2x=1$

a)

$\frac{\pi}{2}+\pi k;\ \frac{\pi}{4}+\pi k$

b)

$\frac{\pi}{4}+\pi k;\ \frac{\pi}{2}+\pi k$

c)

$\frac{\pi}{2}+\pi k;\ \frac{\pi}{4}+2\pi k$

d)

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

38.

$\sin^4x+\cos^4x=\sin x\cdot\cos x$

a)

$\frac{\pi}{4}+2\pi n$

b)

$\frac{\pi}{2}+\pi n$

c)

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

d)

$\frac{\pi}{4}+\pi n$

39.

$\cos2x=2\sin^2x$

a)

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

b)

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

c)

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

d)

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

40.

a)

$30\degree$

b)

$45\degree$

c)

$135\degree$

d)

$225\degree$

41.

a)

$\left(\frac{7}{6}+2k\ ;\ \frac{1}{6}+2k\right),\ \left(\frac{5}{6}+2k\ ;\ -\frac{1}{6}+2k\right),\ k\in Z$

b)

$\left(\frac{7}{6}+k\ ;\ -\frac{1}{6}+k\right),\ \left(\frac{5}{6}+k\ ;\ \frac{1}{6}+k\right),\ k\in Z$

c)

$\left(\frac{7}{3}+k\ ;\ \frac{1}{3}+k\right),\ \left(\frac{5}{3}+k\ ;\ -\frac{1}{3}+k\right),\ k\in Z$

d)

$\left(\frac{7}{6}+k\ ;\ \frac{1}{6}+k\right),\ \left(\frac{5}{6}+k\ ;\ -\frac{1}{6}+k\right),\ k\in Z$

42.

$-\frac{\sqrt{3}}{2}\le\cos x<\frac{2}{3}$

a)

$\left[-\frac{5\pi}{6}+2\pi k;\ -\arccos\ \frac{2}{3}+2\pi k\right]\cup\left[\arccos\ \frac{2}{3}+2\pi k;\ \frac{5\pi}{6}+2\pi k\right],\ k\in Z$

b)

$\left[-\frac{5\pi}{6}+\pi k;\ -\arccos\ \frac{2}{3}+\pi k\right]\cup\left[\arccos\ \frac{2}{3}+\pi k;\ \frac{5\pi}{6}+\pi k\right],\ k\in Z$

c)

$\left[-\frac{5\pi}{6}+2\pi k;\ -\arccos\ \frac{2}{3}+2\pi k\right]\cap\left[\arccos\ \frac{2}{3}+2\pi k;\ \frac{5\pi}{6}+2\pi k\right],\ k\in Z$

d)

$\left[-\frac{5\pi}{3}+2\pi k;\ -\arccos\ \frac{2}{3}+2\pi k\right]\cup\left[\arccos\ \frac{2}{3}+2\pi k;\ \frac{5\pi}{3}+2\pi k\right],\ k\in Z$

43.

$3\cos2x\le2$

a)

$\left[\frac{1}{2}\arccos\ \frac{2}{3}+\pi k;\ \pi-\ \frac{1}{2}\arccos\ \frac{2}{3}+\pi k\right],\ k\in Z$

b)

$\left[\arccos\ \frac{2}{3}+\pi k;\ \pi-\ \arccos\ \frac{2}{3}+\pi k\right],\ k\in Z$

c)

$\left[\frac{1}{2}\arccos\ \frac{2}{3}+\pi k;\ \pi+\ \frac{1}{2}\arccos\ \frac{2}{3}-\pi k\right],\ k\in Z$

d)

$\left[\frac{1}{2}\arccos\ \frac{2}{3}+2\pi k;\ \pi-\ \frac{1}{2}\arccos\ \frac{2}{3}+2\pi k\right],\ k\in Z$

44.

$\sin x>\cos x$

a)

$\left[\frac{\pi}{4}-2\pi n;\frac{5\pi}{4}+2\pi n\right]$

b)

$\left[\frac{\pi}{4}-\pi n;\frac{5\pi}{4}-2\pi n\right]$

c)

$\left[\frac{\pi}{4}+2\pi n;\frac{5\pi}{4}+2\pi n\right]$

d)

$\left[\frac{\pi}{2}+\pi n;\frac{5\pi}{4}+2\pi n\right]$

45.

$\sin^2x>2\cos^2x$

a)

$\left(\pi+2\pi k;2\pi-2\pi k\right)$

b)

$\left(\pi+2\pi k;2\pi+2\pi k\right)$

c)

$\left(\pi-2\pi k;2\pi+2\pi k\right)$

d)

$\left(\pi-2\pi k;2\pi-2\pi k\right)$

46.

$3\sin x>2\cos^2x$

a)

$\left(-\frac{\pi}{6}+2\pi n;\frac{5\pi}{6}+2\pi n\right)$

b)

$\left(\frac{\pi}{6}+2\pi n;\frac{5\pi}{4}+2\pi n\right)$

c)

$\left(\frac{\pi}{6}+2\pi n;\frac{5\pi}{6}+2\pi n\right)$

d)

$\left(\frac{\pi}{6}+\pi n;\frac{5\pi}{6}+\pi n\right)$

47.

$\sin\ x\ >\ \cos x$

a)

$\left[\frac{\pi}{4}+2\pi n;\frac{5\pi}{4}+2\pi n\right]$

b)

$\left[\frac{\pi}{4}+\pi n;\frac{5\pi}{4}+\pi n\right)$

c)

$\left(-\frac{\pi}{4}+2\pi n;\frac{\pi}{4}+2\pi n\right)$

d)

$\left(\frac{\pi}{4}+2\pi n;\frac{3\pi}{4}+2\pi n\right]$

48.

$2\sin^2x+\sqrt{3cin\ x}\ -3>0$

a)

$\left(\frac{\pi}{3}+2\pi n;\frac{2\pi}{3}+2\pi n\right)$

b)

$\left(-\frac{\pi}{3}+2\pi n;\frac{2\pi}{3}+2\pi n\right)$

c)

$\left(\frac{\pi}{3}+2\pi n;\frac{5\pi}{4}+2\pi n\right)$

d)

$\left(\frac{\pi}{4}+2\pi n;\frac{2\pi}{3}+2\pi n\right)$

49.

$2\sin\left(2019\pi+2x\right)\le3$

a)

$\left(1.5,+\infty\right)$

b)

$\left(-\infty,1.5\right)$

c)

$\left(-\infty,2\right)$

d)

$\left(-\infty,+\infty\right)$

50.

$2tg^22x-1>0$

a)

$\left(-\frac{\pi}{4}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{2}}+\frac{\pi k}{2}\div\frac{\pi}{4}+\frac{\pi k}{2}\right)$

b)

$\left(-\frac{\pi}{4}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{3}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{3}}+\frac{\pi k}{2}\div\frac{\pi}{4}+\frac{\pi k}{2}\right)$

c)

$\left(\frac{\pi}{2}+\frac{\pi k}{2};-\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{2}}+\frac{\pi k}{2}\div\frac{\pi}{4}+\frac{\pi k}{2}\right)$

d)

$\left(\frac{\pi}{4}+\frac{\pi k}{4};-\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{2}}+\frac{\pi k}{2}\right)\cup\left(\frac{1}{2}ar\operatorname{ctg}\frac{1}{\sqrt{2}}+\frac{\pi k}{2}\div\frac{\pi}{4}+\frac{\pi k}{2}\right)$

51.

$\cos2x<\cos4x$

a)

$\left(\frac{\pi}{3}+\pi n;\frac{2\pi}{3}+\pi n\right)$

b)

$\left(-\frac{\pi}{3}+\pi n;\frac{2\pi}{3}+\pi n\right)$

c)

$\left(-\frac{\pi}{6}+\pi n;\frac{\pi}{3}+\pi n\right)$

d)

$\left(\frac{\pi}{6}+\pi n;\frac{2\pi}{3}+\pi n\right)$

52.

$\sin2x+\sqrt{3}\ \cos2x\ge1$

a)

$\left[-\frac{\pi}{12}+\pi k;\frac{\pi}{4}+\pi k\right]$

b)

$\left[\frac{\pi}{18}+\pi k;\frac{\pi}{4}+\pi k\right]$

c)

$\left[-\frac{\pi}{12}+\pi k;\frac{\pi}{3}+\pi k\right]$

d)

$\left[-\frac{\pi}{18}+\pi k;\frac{\pi}{4}+\pi k\right]$

53.

$\sin2x\le-\cos2x$

a)

$\left[\frac{3\pi}{8}+\pi k;\frac{7\pi}{8}+\pi k\right]$

b)

$\left[\frac{3\pi}{4}+\pi k;\frac{7\pi}{4}+\pi k\right]$

c)

$\left[\frac{3\pi}{2}+\pi k;\frac{5\pi}{2}+\pi k\right]$

d)

$\left[\frac{3\pi}{4}+\pi k;\frac{\pi}{8}+\pi k\right]$

54.

$tg2x\ge1$

a)

$\left[\frac{\pi}{3}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right]$

b)

$\left[\frac{\pi}{6}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right]$

c)

$\left[\frac{\pi}{8}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right]$

d)

$\left[-\frac{\pi}{3}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right]$

55.

$\sin2x\le-\cos2x$

a)

$\left[\frac{3\pi}{8}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right)$

b)

$\left[\frac{3\pi}{2}+\frac{\pi n}{2};\frac{\pi}{6}+\frac{\pi n}{2}\right)$

c)

$\left[\frac{5\pi}{8}+\frac{\pi n}{2};\frac{\pi}{4}+\frac{\pi n}{2}\right)$

d)

$\left[\frac{3\pi}{4}+\frac{\pi n}{2};\frac{\pi}{3}+\frac{\pi n}{2}\right)$

56.

$\operatorname{ctg}\left(x+\frac{\pi}{3}\right)<-1$

a)

$\left(-\frac{\pi}{3}+2\pi n;\ \frac{5\pi}{12}+2\pi n\right)$

b)

$\left(-\frac{\pi}{3}+\pi n;\ \frac{5\pi}{12}+\pi n\right)$

c)

$\left(-\frac{2\pi}{3}+\pi n;\ \frac{5\pi}{6}+\pi n\right)$

d)

$\left(-\frac{\pi}{3}+\pi n;\ \frac{\pi}{3}+\pi n\right)$

57.

$\sin x-\cos x=\sqrt{2}\cos3x$

a)

$\frac{3\pi}{14}+\frac{\pi k}{2}\cdot\frac{5\pi}{8}+\pi k,\ k\in Z$

b)

$\frac{3\pi}{16}+\pi k\cdot\frac{5\pi}{8}+2\pi k,\ k\in Z$

c)

$-\frac{3\pi}{16}+\frac{\pi k}{2}\cdot\frac{5\pi}{8}+\pi k,\ k\in Z$

d)

$\frac{3\pi}{16}+\frac{\pi k}{2}\cdot\frac{5\pi}{8}+\pi k,\ k\in Z$

58.

$\left(6-x\right)^4+\left(8-x\right)^4=16$

a)

$3;\ 4;\ \sqrt{18};2\sqrt{16}$

b)

$6;\ 8;\ \sqrt{36};\ \sqrt{16}$

c)

$6;\ 4;\ \sqrt{36};\ \sqrt{16}$

d)

$6;\ 8;\ \sqrt{36};\ 2\sqrt{16}$

59.

a)

$\frac{2}{7}$

b)

$\frac{4}{7}$

c)

$-\frac{2}{7}$

d)

$-\frac{4}{7}$

60.

$\frac{x^2++x-5}{x}+\frac{3x}{x^2+x-5}+4=0$

a)

$-1-\sqrt{6};\ -1+\sqrt{6};-1;\ 5$

b)

$1-\sqrt{6};\ 1+\sqrt{6};1;-5$

c)

$-1-\sqrt{6};\ -1+\sqrt{6};1;-5$

d)

$-1-\sqrt{6};\ -1+\sqrt{6};-1;-5$

61.

$\frac{x}{x+1}+\frac{x+1}{x+2}+\frac{x+2}{x}=3$

a)

$\frac{4}{3};\ 1\ \frac{1}{3}$

b)

$-\frac{4}{5};\ -1\ \frac{2}{3}$

c)

$-\frac{4}{3};\ 1\ \frac{1}{3}$

d)

$-\frac{4}{3};\ -1\ \frac{1}{3}$

62.

$2\left(x-\frac{1}{x}\right)+3\left(x^2+\frac{1}{x^2}\right)=11$

a)

$\frac{1-\sqrt{5}}{4};\ \frac{1+\sqrt{5}}{4}$

b)

$\frac{1-\sqrt{5}}{2};\ \frac{1+\sqrt{5}}{2}$

c)

$\frac{1-2\sqrt{5}}{2};\ \frac{1+2\sqrt{5}}{2}$

d)

$\frac{1-\sqrt{5}}{3};\ \frac{1+\sqrt{5}}{3}$

63.

$\left|x^2-x+3\right|=x+2$

a)

2

b)

0

c)

1

d)

-1

64.

$f\left(x\right)=x^2\cdot\left(x-1\right)^2-6x\left(x+1\right)\ болса,\ f'\left(x\right)=-18\ теңдеуінің\ түбірлері$

a)

2; 1; -1.5

b)

3; 0; 2

c)

2; -1; -1.5

d)

2; 1; 1.5

65.

$\frac{1}{4}<\frac{1}{x}<\frac{1}{3}$

a)

(2; 0)

b)

(-3; 4)

c)

$\left(3;\ 4\right)$

d)

(2; 4)

66.

a)

(-6;6)

b)

(-6;0)

c)

(0;6)

d)

[-6;0]

67.

$\frac{1}{3^x+5}\le\frac{1}{3^{x+1}-1}$

a)

(-1;1]

b)

(-1;1)

c)

[0;1]

d)

(0;1)

68.

$\frac{x^3-4x^2-x+4}{x^2-7x+12}\ge0$

a)

$\left(-3;4\right)\left(4;+\infty\right)\left[-1;1\right]$

b)

$\left(3;4\right)\left(-4;+\infty\right)\left[1;1\right]$

c)

$\left(3;4\right)\left(4;+\infty\right)$

d)

$\left(3;4\right)\left(4;+\infty\right)\left[-1;1\right]$

69.

$\frac{2-x}{x^3+x^2}>\frac{1-2x}{x^2-3x^2}$

a)

$\left(-\infty;\ -7\right)\left(3;\ +\infty\right)$

b)

$\left(-\infty;\ -7\right),\ \left(-1;\ 0\right),0$

c)

$\left(-\infty;\ -7\right),\ \left(-1;\ 0\right),\left(3;\ +\infty\right)$

d)

$\left(-\infty;\ -7\right),0$

70.

$\log_{0.3}\log_3\ \frac{x}{x-1}\ge0$

a)

$\left(1.5;+\infty\right]$

b)

$\left[1.5;+\infty\right)$

c)

$\left[1.5;+\infty\right)$

d)

$\left(-1.5;+\infty\right)$

71.

a)

$\left(-\infty;0\right]$

b)

$\left(-\infty;1\right]$

c)

$\left(-\infty;2\right]$

d)

$\left(-\infty;-1\right]$

Тригонометрия

Total questions: 71

Worksheet time: 2hrs 22mins

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