Trắc nghiệm Phương trình lượng giác cơ bản Toán Lớp 11

A. $x=\frac{5\pi}{6} \text {. }$

B. $x=\frac{\pi}{6} \text {. }$

C. $x=\frac{4\pi}{3} \text {. }$

D. $x=\frac{\pi}{3} \text {. }$

A. 21

B. 3

C. 12

D. 14

A. $5\pi$

B. $3\pi$

C. $\pi$

D. $-2\pi$

A. $2\pi$

B. $32\pi$

C. $9\pi$

D. $11\pi$

A. 21

B. $45\pi$

C. $27\pi$

D. $36\pi$

A. 2

B. 0

C. 1

D. 4

A. $x=\pm \frac{2 \pi}{3}+k 4 \pi, k \in \mathbb{Z} \text {. }$

B. $x= \frac{2 \pi}{3}+k 4 \pi, k \in \mathbb{Z} \text {. }$

C. $x=- \frac{2 \pi}{3}+k 4 \pi, k \in \mathbb{Z} \text {. }$

D. $x=\pm \frac{ \pi}{3}+k 4 \pi, k \in \mathbb{Z} \text {. }$

A. 1

B. 2

C. 3

D. 0

A. 1

B. 6

C. 5

D. 7

A. $-\frac{\pi}{4} \text {. }$

B. $-\frac{\pi}{3} \text {. }$

C. $-\frac{\pi}{6} \text {. }$

D. $-\frac{5\pi}{6} \text {. }$

A. 1

B. 2

C. 3

D. 4

A. 2

B. 4

C. 6

D. 8

A. $x=\frac{1}{6}+k, k \in \mathbb{Z} .$

B. $x=\frac{1}{12}+k, k \in \mathbb{Z} .$

C. $x=\frac{\pi}{3}+k, k \in \mathbb{Z} .$

D. $x=\frac{\pi}{12}+k, k \in \mathbb{Z} .$

A. 3

B. 5

C. 6

D. 7

A. $\begin{array}{llll} \cos x=\frac{\sqrt{2}}{2} \end{array}$

B. $\sin x=\frac{\sqrt{2}}{2}$

C. $\tan ^{2} x=1 \text {. }$

D. $\tan x=1 \text {. }$

A. 1

B. 2

C. 10

D. 16

A. $\frac{\pi^{2}}{3}$

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

C. $\frac{\pi^{2}}{4}$

D. $\frac{\pi^{2}+1}{3}$

A. 2018

B. 4036

C. 4001

D. 4343

A. 16

B. 8

C. 5

D. 12

A. $0\leq m \leq 1.$

B. $0 \leq m \leq \frac{2}{3} \text {. }$

C. $-\frac{2}{3} \leq m \leq \frac{2}{3} \text {. }$

D. $-\frac{1}{3} \leq m \leq \frac{2}{3} \text {. }$

A. 999

B. 1000

C. 1001

D. 1002

A. $S=\left\{\frac{\pi}{6} ; \frac{5 \pi}{6} ; \frac{3 \pi}{2} ; \frac{7 \pi}{10}\right\} \text {. }$

B. $S=\left\{\frac{\pi}{6} ; \frac{5 \pi}{4} ; \frac{3 \pi}{10} ; \frac{7 \pi}{10}\right\} \text {. }$

C. $S=\left\{\frac{\pi}{6} ; \frac{5 \pi}{6} ; \frac{3 \pi}{4} ; \frac{7 \pi}{10}\right\} \text {. }$

D. $S=\left\{\frac{\pi}{6} ; \frac{5 \pi}{6} ; \frac{3 \pi}{10} ; \frac{7 \pi}{10}\right\} \text {. }$

A. $\left[\begin{array}{l} x=\frac{\pi}{2}+k 2 \pi \\ x=-\frac{\pi}{5}+\frac{k 2 \pi}{9} \end{array} .\right.$

B. $\left[\begin{array}{l} x=\frac{\pi}{2}+k 2 \pi \\ x=-\frac{\pi}{18}+\frac{k 2 \pi}{9} \end{array} .\right.$

C. $\left[\begin{array}{l} x=\frac{\pi}{2}+k 2 \pi \\ x=\frac{3\pi}{4}+\frac{k 2 \pi}{9} \end{array} .\right.$

D. $\left[\begin{array}{l} x=\frac{\pi}{2}+k 2 \pi \\ x=-\frac{\pi}{3}+\frac{k 2 \pi}{9} \end{array} .\right.$

A. $x=20^{\circ}+k 90^{\circ}(k \in \mathbb{Z})$

B. $x=90^{\circ}+k 90^{\circ}(k \in \mathbb{Z})$

C. $x=30^{\circ}+k 90^{\circ}(k \in \mathbb{Z})$

D. $x=45^{\circ}+k 90^{\circ}(k \in \mathbb{Z})$

A. $x=\frac{\pi}{3}+k \pi(k \in \mathbb{Z})$

B. $x=-\frac{\pi}{4}+k \pi(k \in \mathbb{Z})$

C. $x=\frac{3\pi}{4}+k \pi(k \in \mathbb{Z})$

D. $x=\frac{\pi}{4}+k \pi(k \in \mathbb{Z})$

A. $\begin{array}{ll} \tan x=99 . \end{array}$

B. $\cos \left(2 x-\frac{\pi}{2}\right)=\frac{2 \pi}{3} .$

C. $\cot 2018 x=2017 .$

D. $\sin 2 x=-\frac{3}{4}$

A. $2 \cos x+1=0$

B. $2 \sin x+1=0$

C. $2 \cos x-1=0$

D. $2 \sin x+\sqrt{3}=0$

A. 1

B. 3

C. 4

D. 5

A. $x=30^{\circ}+k 180^{\circ},(k \in \mathbb{Z}) \text {. }$

B. $x=15^{\circ}+k 180^{\circ},(k \in \mathbb{Z}) \text {. }$

C. $x=135^{\circ}+k 180^{\circ},(k \in \mathbb{Z}) \text {. }$

D. $x=45^{\circ}+k 180^{\circ},(k \in \mathbb{Z}) \text {. }$

A. $-k \frac{\pi}{3}$

B. $k \frac{\pi}{3}$

C. $\frac{\pi}{5}$

D. $\frac{\pi}{3}$

A. 6

B. 7

C. 1

D. 9

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

B. $x=\pm \frac{\pi}{45}+\frac{k 2 \pi}{3} \text {. }$

C. $x=\pm \frac{\pi}{3}+\frac{k 2 \pi}{3} \text {. }$

D. $x=\pm \frac{\pi}{15}+\frac{k 2 \pi}{3} \text {. }$

A. $\left[\begin{array}{l} x=\frac{\pi}{6}+k_{1} 2 \pi \\ x=\frac{5 \pi}{6}+k_{2} 2 \pi \\ x=\pm \frac{\pi}{3}+k_{3} \pi . \end{array}\right.$

B. $\left[\begin{array}{l} x=\frac{\pi}{6}+k_{1} 2 \pi \\ x=\frac{5 \pi}{6}+k_{2} 2 \pi \end{array}\right.$

C. $\left[\begin{array}{l} x=\frac{7\pi}{6}+k_{1} 2 \pi \\ x=\frac{5 \pi}{6}+k_{2} 2 \pi \\ x=\pm \frac{\pi}{3}+k_{3} \pi . \end{array}\right.$

D. $\left[\begin{array}{l} x=\frac{\pi}{6}+k_{1} 2 \pi \\ x=\frac{5 \pi}{6}+k_{2} 2 \pi \\ x= \frac{\pi}{3}+k_{3} \pi . \end{array}\right.$

A. $\left[ {\begin{array}{*{20}{l}} {x = \pm \arccos \left( {\frac{2}{3}} \right) + {k_1}2\pi }\\ {x = \frac{\pi }{{12}} + {k_2}\pi }\\ {x = \frac{{5\pi }}{{12}} + {k_3}\pi } \end{array}} \right.$

B. $\left[ {\begin{array}{*{20}{l}} {x = \pm \arccos \left( {\frac{2}{3}} \right) + {k_1}2\pi }\\ {x = \frac{\pi }{{7}} + {k_2}\pi }\\ {x = \frac{{5\pi }}{{12}} + {k_3}\pi } \end{array}} \right.$

C. $\left[ {\begin{array}{*{20}{l}} {x = \frac{\pi }{{2}} + {k_2}\pi }\\ {x = \frac{{5\pi }}{{12}} + {k_3}\pi } \end{array}} \right.$

D. $\left[ {\begin{array}{*{20}{l}} {x = \frac{\pi }{{12}} + {k_2}\pi }\\ {x = \frac{{5\pi }}{{12}} + {k_3}\pi } \end{array}} \right.$

A. $\left[ {\begin{array}{*{20}{l}} {x = \frac{\pi }{2} + {k_1}\pi }\\ {x = \frac{\pi }{{24}} + {k_2}\frac{\pi }{2}} \end{array}} \right.$

B. $\left[ {\begin{array}{*{20}{l}} {x = \frac{\pi }{2} + {k_1}\pi }\\ {x = \frac{\pi }{{24}} + {k_2}\frac{\pi }{2}}\\ {x = \frac{{5\pi }}{{24}} + {k_3}\frac{\pi }{2}} \end{array}} \right.$

C. $\left[ {\begin{array}{*{20}{l}} {x = \frac{\pi }{2} + {k_1}\pi }\\ {x = \frac{7\pi }{{12}} + {k_2}\frac{\pi }{2}}\\ {x = \frac{{5\pi }}{{24}} + {k_3}\frac{\pi }{2}} \end{array}} \right.$

D. $\left[ {\begin{array}{*{20}{l}} {x = \frac{\pi }{2} + {k_1}\pi }\\ {x = \frac{\pi }{{12}} + {k_2}\frac{\pi }{2}}\\ {x = \frac{{5\pi }}{{24}} + {k_3}\frac{\pi }{2}} \end{array}} \right.$

A. $\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} 2 \pi \\ x=-\frac{5 \pi}{12}+k_{2} \frac{2 \pi}{3} \end{array}\right.$

B. $\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} 2 \pi \\ x=\frac{5 \pi}{12}+k_{2} \frac{2 \pi}{3} \end{array}\right.$

C. $\left[\begin{array}{l} x=\frac{3\pi}{4}+k_{1} 2 \pi \\ x=\frac{5 \pi}{12}+k_{2} \frac{2 \pi}{3} \end{array}\right.$

D. $\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} 2 \pi \\ x=\frac{ \pi}{12}+k_{2} \frac{2 \pi}{3} \end{array}\right.$

A. $\left[\begin{array}{l} x=\pi+k_{1} 2 \pi \\ x=-\frac{3\pi}{4}+k_{2} \pi \end{array}\right.$

B. $\left[\begin{array}{l} x=\pi+k_{1} 2 \pi \\ x=-\frac{7\pi}{4}+k_{2} \pi \end{array}\right.$

C. $\left[\begin{array}{l} x=\pi+k_{1} 2 \pi \\ x=-\frac{\pi}{4}+k_{2} \pi \end{array}\right.$

D. $x=\pi+k_{1} 2 \pi$

A. $x=\frac{\pi}{4}+k_{1} \frac{\pi}{2} .$

B. $x=\frac{3\pi}{4}+k_{1} \frac{\pi}{2} .$

C. $x=\frac{5\pi}{4}+k_{1} \frac{\pi}{2} .$

D. $x=\frac{7\pi}{4}+k_{1} \frac{\pi}{2} .$

A. Vô nghiệm.

B. $\left[ {\begin{array}{*{20}{l}} {x = - \frac{2\pi }{4} + {k_1}2\pi }\\ {x = {k_2}\frac{\pi }{2}} \end{array}} \right.$

C. $\left[ {\begin{array}{*{20}{l}} {x = - \frac{3\pi }{4} + {k_1}\pi }\\ {x = {k_2}\frac{\pi }{2}} \end{array}} \right.$

D. $\left[ {\begin{array}{*{20}{l}} {x = - \frac{\pi }{4} + {k_1}\pi }\\ {x = {k_2}\frac{\pi }{2}} \end{array}} \right.$

A. $\left[\begin{array}{l} x=-\frac{\pi}{4}+k_{1} \pi \\ x= \frac{\pi}{3}+k_{2} \pi \end{array}\right.$

B. $\left[\begin{array}{l} x=-\frac{\pi}{4}+k_{1} \pi \\ x=\pm \frac{\pi}{3}+k_{2} 2 \pi \end{array}\right.$

C. $\left[\begin{array}{l} x=-\frac{5\pi}{4}+k_{1} \pi \\ x=\pm \frac{2\pi}{3}+k_{2} 2 \pi \end{array}\right.$

D. $\left[\begin{array}{l} x=-\frac{\pi}{4}+k_{1} \pi \\ x=\pm \frac{2\pi}{3}+k_{2} 2 \pi \end{array}\right.$

A. $\left[\begin{array}{l} x=-\frac{\pi}{4}+k_{1} \pi \\ x=\frac{\pi}{6}+k_{2} 2 \pi \\ x=\frac{5 \pi}{6}+k_{3} 2 \pi \end{array}\right.$

B. $\left[\begin{array}{l} x=-\frac{\pi}{4}+k_{1} \pi \\ x=\frac{7\pi}{6}+k_{2} 2 \pi \\ x=\frac{5 \pi}{6}+k_{3} 2 \pi \end{array}\right.$

C. $\left[\begin{array}{l} x=-\frac{\pi}{4}+k_{1} \pi \\ x=\pm\frac{\pi}{6}+k_{2} 2 \pi \\ x=\frac{5 \pi}{6}+k_{3} 2 \pi \end{array}\right.$

D. $\left[\begin{array}{l} x=-\frac{\pi}{4}+k_{1} \pi \\ x=\frac{5\pi}{6}+k_{2} 2 \pi \end{array}\right.$

A. $\quad\left[\begin{array}{l} x=-\frac{\pi}{2}+k_{1} 2 \pi \\ x= \frac{\pi}{3}+k_{2} 2 \pi \end{array}\right.$

B. $\quad\left[\begin{array}{l} x=-\frac{\pi}{2}+k_{1} 2 \pi \\ x=\pm \frac{\pi}{3}+k_{2} 2 \pi \end{array}\right.$

C. $\quad\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} 2 \pi \\ x=\pm \frac{\pi}{3}+k_{2} 2 \pi \end{array}\right.$

D. $\quad\left[\begin{array}{l} x=-\frac{\pi}{2}+k_{1} \pi \\ x=\pm \frac{\pi}{3}+k_{2} 2 \pi \end{array}\right.$

A. $x=k 2 \pi$

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

C. $x=\frac{\pi}{2}+k 2 \pi$

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

A. $\left[\begin{array}{l} x=\frac{\pi}{12}+k_{1} \pi \\ x=\frac{5 \pi}{6}+k_{2} \pi \end{array}\right.$

B. $\left[\begin{array}{l} x=\frac{\pi}{12}+k_{1} \pi \\ x=\frac{5 \pi}{6}+k_{2} \pi \\ x=\frac{\pi}{3}+k_{3} 2 \pi \end{array}\right.$

C. $\left[\begin{array}{l} x=\frac{7\pi}{12}+k_{1} \pi \\ x=\frac{5 \pi}{12}+k_{2} \pi \\ x=\pm \frac{\pi}{3}+k_{3} 2 \pi \end{array}\right.$

D. $\left[\begin{array}{l} x=\frac{\pi}{12}+k_{1} \pi \\ x=\frac{5 \pi}{12}+k_{2} \pi \\ x=\pm \frac{\pi}{3}+k_{3} 2 \pi \end{array}\right.$

A. $x=-\frac{3\pi}{4}+k \pi$

B. $x=-\frac{\pi}{4}+k \pi$

C. $x=-\frac{\pi}{3}+k \pi$

D. $x=\pm\frac{\pi}{4}+k \pi$

A. $\left[\begin{array}{l} x=\frac{3\pi}{4}+k_{1} \frac{\pi}{2} \\ x=\frac{\pi}{2}+k_{2} \pi \end{array}\right.$

B. Vô nghiệm.

C. $\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} \frac{\pi}{2} \\ x=\frac{\pi}{2}+k_{2} \pi \end{array}\right.$

D. $x=\frac{\pi}{4}+k_{1} \frac{\pi}{2}$

A. ${\left[\begin{array}{l} x=k 2 \pi \\ x=\frac{\pi}{6}+k^{\prime} \frac{ \pi}{3} . \end{array}\right.}$

B. ${\left[\begin{array}{l} x=k 2 \pi \\ x=\frac{\pi}{3}+k^{\prime} \frac{2 \pi}{3} . \end{array}\right.}$

C. ${\left[\begin{array}{l} x=k 2 \pi \\ x=\frac{\pi}{4}+k^{\prime} \frac{2 \pi}{3} . \end{array}\right.}$

D. ${\left[\begin{array}{l} x=k 2 \pi \\ x=\frac{\pi}{6}+k^{\prime} \frac{2 \pi}{3} . \end{array}\right.}$

A. $\left[\begin{array}{l} x=k_{1} \pi \\ x=-\frac{\pi}{4}+k_{2} \frac{\pi}{2} \end{array}\right.$

B. $\left[\begin{array}{l} x=k_{1} \pi \\ x=-\frac{\pi}{8}+k_{2} \frac{\pi}{2} \end{array}\right.$

C. $\left[\begin{array}{l} x=k_{1} \pi \\ x=-\frac{\pi}{2}+k_{2} \frac{\pi}{2} \end{array}\right.$

D. $\left[\begin{array}{l} x=k_{1} \pi \\ x=-\frac{3\pi}{8}+k_{2} \frac{\pi}{2} \end{array}\right.$

A. $x=\frac{\pi}{4}+k_{1} \frac{\pi}{2}$

B. $\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} \frac{\pi}{2} \\ x=\frac{\pi}{6}+k_{2}2 \pi \end{array}\right.$

C. $\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} \frac{\pi}{2} \\ x=\frac{\pi}{6}+k_{2} \pi \end{array}\right.$

D. $\left[\begin{array}{l} x=\frac{\pi}{4}+k_{1} \frac{\pi}{2} \\ x=-\frac{\pi}{6}+k_{2} \pi \end{array}\right.$

A. $\left[\begin{array}{l} x=\frac{3 \pi}{4}+k_{1} \pi \\ x=\frac{\pi}{6}+k_{2} 2 \pi \\ x=\frac{5 \pi}{6}+k_{3} 2 \pi \end{array}\right.$

B. $\left[\begin{array}{l} x=\frac{3 \pi}{4}+k_{1} \pi \\ x=\frac{\pi}{6}+k_{2} 2 \pi \end{array}\right.$

C. $\left[\begin{array}{l} x=\frac{3 \pi}{4}+k_{1} \pi \\ x=\frac{5 \pi}{6}+k_{3} 2 \pi \end{array}\right.$

D. $\left[\begin{array}{l} x=\frac{3 \pi}{2}+k_{1} \pi \\ x=\frac{\pi}{6}+k_{2} 2 \pi \\ x=\frac{5 \pi}{6}+k_{3} 2 \pi \end{array}\right.$