Free Printable Жаңа тригонометрия Балмира

1.

$4\sin^33x-\sin3x=2+\sin^3x$

a)

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

b)

$x=\frac{\pi}{6}+\frac{2\pi n}{3};\ x=\left(-1\right)^{k+1}\ \frac{1}{3}\arcsin\ \frac{2}{3}+\frac{\pi n}{3}$

c)

$x=\frac{\pi}{6}+\frac{\pi}{3}\ x=\ \arcsin\ \frac{1}{3}+2\pi$

d)

$x=\frac{\pi}{6}+\frac{2\pi}{3}n\ ;\ x=\frac{2}{3}\arcsin\frac{1}{3}+\frac{\pi n}{3}$

2.

$2\cos^2x-5\cos x=-3$

a)

$2\pi n$

b)

$4\pi n$

c)

$\pi n$

d)

$\frac{\pi}{2}$

3.

$\cos^23x=\frac{1}{2}$

a)

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

b)

$\frac{\pi}{12}+\frac{\pi k}{6}$

c)

$\frac{\pi}{4}+\frac{\pi n}{6}$

d)

$\frac{\pi}{8}+\frac{\pi n}{8}$

4.

$2\cos2x+\sqrt{3}=0$

a)

$x=\pm\frac{5\pi}{12}+\pi k$

b)

$x=\frac{5\pi}{12}$

c)

$x=\pm\frac{\pi}{12}+\pi k$

d)

$x=\pm\frac{5\pi}{12}+2\pi k$

5.

$6\sin^2x-\cos x-5=0$

a)

$x=\ \arccos\ \frac{1}{3}+\pi k$

b)

$x=\pm\frac{4\pi}{3}+2\pi k$

c)

$x=\pm\frac{2\pi}{3}+2\pi n\ ;\ x=\arccos\ \frac{1}{3}+2\pi k$

d)

$x=\pm\frac{\pi}{3}+\pi k;\ x=\arccos\ \frac{1}{3}+2\pi k$

6.

$6\cos^2x+\sin x-5=0$

a)

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

b)

$x=\left(-1\right)^{k\ }\ \frac{\pi}{6}+2\pi k;\ \ \arcsin\ \frac{1}{3}+2\pi\pi k$

c)

$x=\frac{\pi}{6}+\pi k;\ \frac{2\pi}{3}+\pi n$

d)

$x=\left(-1\right)^k\ \frac{\pi}{6}+\pi n\ ;\left(-1\right)^{k+1\ }\arcsin\ \frac{1}{3}+\pi n$

7.

$\left(\sqrt{2}\sin\ \frac{x}{2}-\sqrt{2\ }\cos\ \frac{x}{2}\right)^2=5+\sin\ \left(\frac{x}{4}-\frac{x}{2}\right)$

a)

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

b)

$\frac{3\pi}{2}+4\pi k$

c)

$\frac{5\pi}{6}+4\pi k$

d)

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

8.

$\sin3x\cos3x=-\frac{1}{2}$

a)

$-\frac{\pi}{12}+\frac{\pi n}{3}$

b)

$\frac{\pi}{12}+\frac{\pi}{3}+\pi k$

c)

$-\frac{\pi}{6}+\frac{\pi k}{3}$

d)

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

9.

$-\sqrt{3}\operatorname{ctg}\left(x+\frac{\pi}{5}\right)=1$

a)

$x=\frac{5\pi}{12}+\pi k$

b)

$x=\frac{7\pi}{15}+\pi k$

c)

$x=\frac{3\pi}{7}+\pi k$

d)

$x=\frac{2\pi}{15}+\pi k$

10.

$\sin\left(\frac{\pi}{3}-2x\right)\cos\left(\frac{\pi}{3}-2x\right)\ge\frac{-\sqrt{3}}{4}$

a)

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

b)

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

c)

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

d)

$\left[-\frac{\pi}{6}+\frac{\pi n}{3};\frac{\pi}{4}+\frac{\pi n}{3}\right]$

11.

$\cos^2x\ge0.25$

a)

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

b)

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

c)

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

d)

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

12.

$-\sqrt{3}\operatorname{ctg}\left(x-\frac{\pi}{5}\right)\le1$

a)

$\frac{\pi}{15}+\pi n;\frac{\pi}{4}+\pi n$

b)

$\frac{\pi}{5}+\pi n$

c)

$-\frac{\pi}{5}+\pi n;\frac{7\pi}{15}+\pi n$

d)

$-\frac{\pi}{12}+\pi n;\frac{\pi}{3}+\pi n$

13.

$2\cos^2\left(x+\frac{\pi}{4}\right)-\sqrt{3}\cos2x\le0$

a)

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

b)

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

c)

$\left[-\frac{\pi}{15}+\pi n;\frac{\pi}{6}+\pi n\right]$

d)

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

14.

\left\{\cos2x\ge0\ \ \ \ \sin2x\ge0\right\}\ \ \ жүйе\ шешіңіз

a)

$\pi n$

b)

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

c)

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

d)

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

15.

$\left(\sin2x+\sqrt{3}\cos2x\right)^2=5+\cos\left(2x-\frac{\pi}{6}\right)$

a)

$\frac{5\pi}{12}+\pi n$

b)

$\frac{7\pi}{12}+\pi n$

c)

$\pi n$

d)

$2\pi n$

16.

sin2xcos6x алғашқы функциясын табыңыз

a)

$\frac{1}{4}\cos4x-\frac{1}{8}\cos8x+4\ ;\ \frac{1}{8}\cos4x-\frac{1}{16}\cos8x+1$

b)

$\frac{1}{2}\cos8x-\frac{1}{2}\sin6x+5\ ;\frac{1}{3}\sin8x+\frac{1}{5}\cos4x+6$

c)

$\frac{1}{16}\cos4x+\frac{1}{8}\sin2x;\ \frac{1}{8}\sin5x+\frac{1}{8}\cos2x$

17.

$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\left(\cos^2\left(x+\frac{\pi}{3}\right)-\sin^2\left(x+\frac{\pi}{3}\right)\right)dx$

a)

$-\frac{\sqrt{2}}{4}$

b)

$\frac{\sqrt{3}}{2}\ немесе\ \sqrt{3}$

c)

$-\frac{\sqrt{3}}{4}\ \ немесе\ -\frac{3}{4\sqrt{3}}$

d)

$\sqrt{3}$

18.

$\sin^27x-\cos^27x=\frac{\sqrt{3}}{2}$

a)

$\pm\frac{5\pi}{84}+\frac{\pi k}{7}$

b)

$\frac{5\pi}{87}+\frac{\pi k}{7}$

c)

$\pm\frac{7\pi}{85}+\frac{\pi}{7}$

d)

$\pm\frac{5\pi}{74}+\frac{\pi k}{7}$

19.

$\left\{\sqrt{2}\sin x+\cos y=1;\ 2\sin x+3\cos y=\sqrt{2}\right\}$ жүйесінің шешімі

a)

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

b)

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

c)

$\left(\left(-1\right)^k\ \frac{\pi}{4}+\pi n;\ \frac{\pi}{2}+\pi n\right)$

20.

$f\left(x\right)=x^2-2x\ ;g\left(x\right)=\sin7x\ f\left(\left(\frac{\pi}{6}\right)\right)=?$

a)

$\frac{4}{5}$

b)

$\frac{5}{4}$

c)

$-\frac{3}{4}$

d)

$-\frac{1}{2}$

21.

$\left\{\sin3x>\frac{1}{2};tgx>\sqrt{3}\right\}\ жүйенің\ шешімі$

a)

$\left(\frac{25\pi}{18}+2\pi n;\ \frac{3\pi}{2}+2\pi n\right)$

b)

$\left(\frac{23\pi}{18}+2\pi n;\frac{3\pi}{2}+2\pi n\right)$

c)

$\left(\frac{25\pi}{16}+\pi n;\frac{2\pi}{3}+2\pi n\right)$

22.

$\cos\left(2x-\frac{\pi}{3}\right)\ge\frac{\sqrt{2}}{2}$

a)

$\frac{\pi}{18}+\pi n$

b)

$\frac{\pi}{24}+\pi n;\frac{7\pi}{24}+\pi n$

c)

$-\frac{\pi}{24}+\pi n;\frac{5\pi}{24}+\pi n$

23.

$\cos\left(\frac{\pi}{3}-2x\right)-\cos\left(\frac{\pi}{6}+2x\right)=1$

a)

$x=\pm\frac{\pi}{4}+\frac{\pi}{24}\pi n$

b)

$x=\pm\frac{\pi}{6}+\frac{5\pi}{28}+\pi n$

c)

$x=\pm\frac{\pi}{8}+\frac{7\pi}{24}+\pi n$

Жаңа тригонометрия Балмира

Total questions: 23

Worksheet time: 12mins

Similar Resources on Wayground