Đề trắc nghiệm ôn tập Chương Hàm số lượng giác và phương trình lượng giác lớp 11

A. \(\left[ { - 1;1} \right]\;\)

B. \(\left[ { - 2;2} \right]\;\)

C. \(R\)

D. \(\left( { - 1;1} \right)\)

A. \(S = \left\{ {\frac{\pi }{2} + k\pi ,k \in Z} \right\}\)

B. \(\left\{ { - \frac{\pi }{2} + k\pi ,k \in Z} \right\}\)

C. \(\left\{ { - \frac{\pi }{2} + k2\pi ,k \in Z} \right\}\)

D. \(\left\{ {\frac{\pi }{2} + k2\pi ,k \in Z} \right\}\)

A. 0

B. 1

C. 2

D. 3

A. \(D = R\backslash \left\{ {k\pi ,k \in Z} \right\}\)

B. \(D = R\backslash \left\{ {\frac{\pi }{2} + k\pi ,k \in Z} \right\}\)

C. \(D = R\backslash \left\{ {\frac{\pi }{2} + k2\pi ,k \in Z} \right\}\)

D. \(D = R\backslash \left\{ {k2\pi ,k \in Z} \right\}\)

A. \(S = \left\{ {\frac{\pi }{2} + k\pi ,k \in Z} \right\}\)

B. \(S = \left\{ {\frac{\pi }{8} + k\pi ,k \in Z} \right\}\)

C. \(S = \left\{ {\frac{\pi }{8} + k\frac{\pi }{4},k \in Z} \right\}\)

D. \(S = \left\{ {\frac{\pi }{8} + k\frac{\pi }{2},k \in Z} \right\}\)

A. \(S = \left\{ {\frac{\pi }{3} + k\pi ,k \in Z} \right\}\)

B. \(S = \left\{ {\frac{\pi }{2} + k\pi ,k \in Z} \right\}\)

C. \(S = \left\{ {\frac{\pi }{2} + k2\pi ,k \in Z} \right\}\)

D. \(S = \left\{ { - \frac{\pi }{6} + k\pi ,k \in Z} \right\}\)

A. \(x =  - \frac{\pi }{3}\)

B. \(x =  - \frac{\pi }{6}\)

C. \(x =  - \frac{{5\pi }}{6}\)

D. \(x = \frac{{ - \pi }}{4}\)

A. \(x= \pm \frac{\pi }{6} + k\pi \)

B. \(x= \pm \frac{\pi }{3} + k\pi \)

C. \(x=\frac{1}{{10}} + \frac{k}{5}\)

D. \(x= \pm \frac{{2\pi }}{9} + \frac{{k\pi }}{3}\)

A. 2

B. 4

C. 3

D. 5

A. 2 lẻ, 2 chẵn 

B. 1 lẻ, 3 chẵn 

C. 4 lẻ 

D. 3 lẻ, 1 chẵn

A. \(\frac{\pi }{{12}} + k\pi \)

B. \(\frac{\pi }{4} + k\pi \)

C. \(\frac{{5\pi }}{8} + k\pi \)

D. \(\frac{\pi }{6} + k\pi \)

A. \(x = \frac{\pi }{4} + k\pi \)

B. \(x = \frac{\pi }{2} + k\pi \)

C. \(x = \frac{\pi }{4} + k\pi ;x = k\pi \)

D. \(x = \frac{\pi }{4} + k\pi ;x = \frac{\pi }{2} + k\pi \)

A. \(x =  - \frac{\pi }{4} + k2\pi ;x = \frac{{5\pi }}{4} + k2\pi \)

B. \(x = \frac{\pi }{3} + k2\pi ;x = \frac{{2\pi }}{3} + k2\pi \)

C. \(x =  - \frac{\pi }{4} + k2\pi ;x = \frac{{3\pi }}{4} + k2\pi \)

D. \(x =  - \frac{\pi }{{12}} + k2\pi ;x = \frac{{5\pi }}{{12}} + k2\pi \)

A. \(x = \frac{\pi }{6} + k\pi \)

B. \(x =  - \frac{\pi }{3} + k\pi \)

C. \(x = \frac{{ - \pi }}{6} + k\pi \)

D. \(x = \frac{\pi }{3} + k\pi \)

A. \(D = R\backslash \left\{ {k\frac{{2\pi }}{3},{\rm{ }}k \in Z} \right\}\)

B. \(D = R\backslash \left\{ {\frac{\pi }{2} + k\frac{\pi }{3},{\rm{ }}k \in Z} \right\}\)

C. \(D = R\backslash \left\{ {\frac{\pi }{2} + k\frac{{2\pi }}{3},{\rm{ }}k \in Z} \right\}\)

D. \(D = R\backslash \left\{ {k\frac{\pi }{3},{\rm{ }}k \in Z} \right\}\)

A. \(D = R\backslash \left\{ {\frac{\pi }{{12}} + k\frac{\pi }{2},\frac{\pi }{6} + k\frac{\pi }{2};{\rm{ }}k \in Z} \right\}\)

B. \(D = R\backslash \left\{ {\frac{\pi }{4} + k\frac{\pi }{2},\frac{\pi }{{12}} + k\frac{\pi }{2};{\rm{ }}k \in Z} \right\}\)

C. \(D = R\backslash \left\{ {\frac{\pi }{4} + k\pi ,\frac{\pi }{{12}} + k\frac{\pi }{2};{\rm{ }}k \in Z} \right\}\)

D. \(D = R\backslash \left\{ {\frac{\pi }{6} + k\frac{\pi }{2};\frac{\pi }{4} + k\frac{\pi }{2}{\rm{ }}k \in Z} \right\}\)

A. \(\max y = 6,\min y =  - 2\)

B. \(\max y = 4,\min y =  - 4\)

C. \(\max y = 6,\min y =  - 4\)

D. \(\max y = 6,\min y =  - 1\)

A. \(x = \frac{\pi }{2} + \frac{{k\pi }}{4},k \in Z\)

B. \(x =  - \frac{\pi }{3} + k\pi ,k \in Z\)

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

D. \(x = \frac{{k\pi }}{4},k \in Z\)

A. \(\left[ \begin{array}{l}
x =  - \frac{1}{8} + k\frac{\pi }{2}\\
x = \frac{\pi }{4} + k\frac{\pi }{2}
\end{array} \right.,k \in Z\)

B. \(\left[ \begin{array}{l}
x =  - \frac{1}{8} - \frac{1}{4}\arcsin \frac{1}{3} + k\frac{\pi }{2}\\
x = \frac{\pi }{4} - \frac{1}{8} - \frac{1}{4}\arcsin \frac{1}{3} + k\frac{\pi }{2}
\end{array} \right.,k \in Z\)

C. \(\left[ \begin{array}{l}
x = \frac{1}{8} - \frac{1}{4}\arcsin \frac{1}{3} + k\frac{\pi }{2}\\
x = \frac{\pi }{4} - \frac{1}{8} - \frac{1}{4}\arcsin \frac{1}{3} + k\frac{\pi }{2}
\end{array} \right.,k \in Z\)

D. \(\left[ \begin{array}{l}
x =  - \frac{1}{8} - \frac{1}{4}\arcsin \frac{1}{3} + k\frac{\pi }{2}\\
x = \frac{\pi }{4} - \frac{1}{4}\arcsin \frac{1}{3} + k\frac{\pi }{2}
\end{array} \right.,k \in Z\)

A. \(\left[ \begin{array}{l}
x = \frac{\pi }{{50}} + \frac{{k2\pi }}{5}\\
x = \frac{{17\pi }}{{90}} + \frac{{k\pi }}{9}
\end{array} \right.\;\left( {k \in Z} \right)\)

B. \(\left[ \begin{array}{l}
x =  - \frac{{3\pi }}{{50}} + \frac{{k2\pi }}{5}\\
x = \frac{{17\pi }}{{30}} + \frac{{k\pi }}{9}
\end{array} \right.\;\left( {k \in Z} \right)\)

C. \(\left[ \begin{array}{l}
x = \frac{\pi }{{50}} + \frac{{k2\pi }}{5}\\
x = \frac{\pi }{{30}} + \frac{{k2\pi }}{9}
\end{array} \right.\;\left( {k \in Z} \right)\)

D. \(\left[ \begin{array}{l}
x = \frac{{3\pi }}{{50}} + \frac{{k2\pi }}{5}\\
x = \frac{{17\pi }}{{90}} + \frac{{k2\pi }}{9}
\end{array} \right.\;\left( {k \in Z} \right)\)

A. Có 1 họ nghiệm 

B. Có 2 họ nghiệm 

C. Vô nghiệm 

D. Có 1 nghiệm duy nhất 

A. \(\left[ \begin{array}{l}
x = k\pi \\
x = \frac{\pi }{3} + k\pi 
\end{array} \right.\left( {k \in Z} \right)\)

B. \(\left[ \begin{array}{l}
x = k\pi \\
x = \frac{{2\pi }}{3} + 2k\pi 
\end{array} \right.\left( {k \in Z} \right)\)

C. \(\left[ \begin{array}{l}
x = 2k\pi \\
x = \frac{{2\pi }}{3} + 2k\pi 
\end{array} \right.\left( {k \in Z} \right)\)

D. \(\left[ \begin{array}{l}
x = k\pi \\
x = \frac{{2\pi }}{3} + k\pi 
\end{array} \right.\left( {k \in Z} \right)\)

A. \(x =  - \frac{\pi }{4} + k\pi ,k \in Z\)

B. \(x =  \pm \frac{\pi }{3} + k\pi ,k \in Z\)

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

D. \(\left[ \begin{array}{l}
x = \frac{\pi }{4} + k\pi \\
x = \frac{\pi }{3} + k\pi 
\end{array} \right.,k \in Z\)

A. \(0 \le m \le \frac{{25}}{8}\)

B. \(0 < m < \frac{{25}}{8}\)

C. \(2 \le m \le \frac{{25}}{8}\)

D. \(2 < m < \frac{{25}}{8}\)

A. \(D = \left[ {0;2\pi } \right]\)

B. \(R\backslash \left\{ { - \frac{\pi }{2} + k2\pi } \right\}\)

C. \(R\backslash \left\{ {\frac{\pi }{2} + k2\pi } \right\}\)

D. \(R\backslash \left\{ { \pm \frac{\pi }{2} + k2\pi } \right\}\)

A. \(y = \sin x\)

B. \(y = {x^2} + \cos 2x\)

C. \(y = \left| {x + \sin x + \tan x} \right|\)

D. \(y = \cos x + \sin x\)

A. \(1\)

B. \(\sqrt 2 \)

C. \(4\)

D. \(2\)

A. \(\forall m \in R\)

B. \( - 2 \le m \le 2\)

C. \( - 1 \le m \le 1\)

D. \(\left[ \begin{array}{l}
m \le  - 1\\
m \ge 1
\end{array} \right.\)

A. \(m \le  - 2\)

B. \(m \ge 2\)

C. \( - 2 \le m \le 2\)

D. \(\left[ \begin{array}{l}
m \le  - 2\\
m \ge 2
\end{array} \right.\)

A. \( - \frac{\pi }{6} + k2\pi \)

B. \( - \frac{\pi }{6} + k\pi \)

C. \(\frac{\pi }{6} + k2\pi \)

D. \(\frac{\pi }{6} + k\pi \)

A. \(\frac{\pi }{2} + k\pi \)

B. \(k2\pi \)

C. \(\pi  + k2\pi \)

D. \(\frac{\pi }{2} + k2\pi \)

A. \(x =  - \frac{\pi }{4} + k2\pi ;x = \frac{{5\pi }}{4} + k2\pi \)

B. \(x = \frac{\pi }{3} + k2\pi ;x = \frac{{2\pi }}{3} + k2\pi \)

C. \(x =  - \frac{\pi }{4} + k2\pi ;x = \frac{{3\pi }}{4} + k2\pi \)

D. \(x =  - \frac{\pi }{{12}} + k2\pi ;x = \frac{{5\pi }}{{12}} + k2\pi \)

A. \(x = \frac{\pi }{2} + k\pi ;x = \arctan 2 + k\pi \)

B. \(x = \arctan 2 + k\pi \)

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

D. \(x = k\pi ;x = \arctan 2 + k\pi )

A. \(x = \frac{\pi }{8} + k\frac{\pi }{2};x = \frac{{7\pi }}{{24}} + k\frac{\pi }{2}\)

B. \(x = k\pi ;x = \pi  + k2\pi \)

C. \(x = k2\pi ;x = \frac{\pi }{2} + k2\pi \)

D. \(x = \pi  + k2\pi ;x = k\frac{\pi }{2}\)

A. \(x = \frac{{5\pi }}{6}\)

B. \(x = \frac{\pi }{6}\)

C. \(x = \pi \)

D. \(x = \frac{\pi }{{12}}\)

A. 4

B. 6

C. 2

D. 8

A. 4

B. 5

C. 6

D. 2

A. \(\left[ \begin{array}{l}
\sin x = 0\\
\sin x = 1
\end{array} \right.\)

B. \(\left[ \begin{array}{l}
\sin x = 0\\
\sin x =  - 1
\end{array} \right.\)

C. \(\left[ \begin{array}{l}
\sin x = 0\\
\sin x = \frac{1}{2}
\end{array} \right.\)

D. \(\left[ \begin{array}{l}
\sin x = 0\\
\sin x =  - \frac{1}{2}
\end{array} \right.\)

A. \(\frac{{{\pi ^2}}}{{16}}\)

B. \( - \frac{{9{\pi ^2}}}{{16}}\)

C. \(\frac{{9{\pi ^2}}}{{16}}\)

D. \( - \frac{{{\pi ^2}}}{{16}}\)

A. 4

B. 8

C. 2

D. 5