Trắc nghiệm Phương trình lượng giác cơ bản Toán Lớp 11

A. \(x = \frac{\pi}2  + 2k\pi \)

B. \(x = \pi  + 2k\pi \)

C. \(x = \frac{\pi}3  + 2k\pi \)

D. \(x = \frac{\pi}4  + 2k\pi \)

A. 1

B. 2

C. 3

D. 4

A. \(x = k\pi ,x =  \pm \arccos \frac{1}{3}   + 2k\pi \).

B. \(x = 2k\pi ,x =  \pm \arccos \frac{1}{3}   + 2k\pi \).

C. \(x = 2k\pi ,x =  \pm \arccos \frac{1}{3}   + k\pi \).

D. \(x = k\pi ,x =  \pm \arccos \frac{1}{3}   + k\pi \).

A. \(x = {\pi  \over {2}} + k{\pi  \over 2}\)

B. \(x = {\pi  \over {4}} + k{\pi  \over 2}\)

C. \(x = {\pi  \over {12}} + 3k{\pi  \over 2}\)

D. \(x = {\pi  \over {12}} + k{\pi  \over 2}\)

A. \(x = {{41\pi } \over {126}} + k{{\pi } \over 3},x = -{{29\pi } \over {126}} + k{{\pi } \over 3}\)

B. \(x = {{41\pi } \over {126}} + k{{2\pi } \over 3},x = -{{29\pi } \over {126}} + k{{2\pi } \over 3}\)

C. \(x = {{41\pi } \over {126}} + k{{\pi } \over 3},x = -{{29\pi } \over {126}} + k{{2\pi } \over 3}\)

D. \(x = {{41\pi } \over {126}} + k{{2\pi } \over 3},x = -{{29\pi } \over {126}} + k{{\pi } \over 3}\)

A. 1 nghiệm

B. 2 nghiệm

C. 3 nghiệm

D. 4 nghiệm

A. \(x = {{7\pi } \over 2}\)

B. \(x = {{71\pi } \over {30}}\)

C. \(x = {{9\pi } \over 2}\)

D. Phương trình không có nghiệm trong khoảng đang xét

A. \({240^o} \in X\)

B. \({290^o} \in X\)

C. \({220^o} \in X\)

D. \({200^o} \in X\)

A. \(x = {{9\pi } \over {16}}\)

B. \(x = {{5\pi } \over {16}}\)

C. \(x = {{21\pi } \over {16}}\)

D. \(x = {{29\pi } \over {16}}\)

A. \(x = {{4\pi } \over 3}\)

B. \(x = {{2\pi } \over 3}\)

C. \(x = {{1\pi } \over 3}\)

D. \(x = {{4\pi } \over 5}\)

A. 0 < m < 2

B. -2 < m < 1

C. 0 < m < 1

D. 0,5 < m < 1

A. - 1 < m < 2

B. 1 < m < 2

C. - 1 < m < 1

D. - 1 < m < 0

A. \(x =  \pm {\pi  \over 3} + k\pi .\)

B. \(x =  \pm {\pi  \over 3} + k2\pi .\)

C. \(x =  \pm {\pi  \over 4} + k2\pi .\)

D. \(x =  \pm {\pi  \over 4} + k\pi .\)

A. 2,59

B. 2,160

C. 0,785

D. 2,95

A. \(x = {\pi  \over {18}} + k{{\pi } \over 3},x = {{7\pi } \over {30}} + k{{2\pi } \over 5},\) \(x =  - {\pi  \over {30}} + k{{2\pi } \over 5},x = {{5\pi } \over {18}} + k{{2\pi } \over 3}\).

B. \(x = {\pi  \over {18}} + k{{2\pi } \over 3},x = {{7\pi } \over {30}} + k{{\pi } \over 5},\) \(x =  - {\pi  \over {30}} + k{{2\pi } \over 5},x = {{5\pi } \over {18}} + k{{2\pi } \over 3}\).

C. \(x = {\pi  \over {18}} + k{{2\pi } \over 3},x = {{7\pi } \over {30}} + k{{2\pi } \over 5},\) \(x =  - {\pi  \over {30}} + k{{2\pi } \over 5},x = {{5\pi } \over {18}} + k{{\pi } \over 3}\).

D. \(x = {\pi  \over {18}} + k{{2\pi } \over 3},x = {{7\pi } \over {30}} + k{{2\pi } \over 5},\) \(x =  - {\pi  \over {30}} + k{{2\pi } \over 5},x = {{5\pi } \over {18}} + k{{2\pi } \over 3}\).

A. \(x =  - {\pi  \over 16} + {{k\pi } \over 2},x = {{-5\pi } \over {16}} + {{k\pi } \over 2}\)

B. \(x =  {\pi  \over 16} + {{k\pi } \over 2},x = {{5\pi } \over {16}} + {{k\pi } \over 2}\)

C. \(x =  - {\pi  \over 6} + {{k\pi } \over 2},x = {{5\pi } \over {16}} + {{k\pi } \over 2}\)

D. \(x =  - {\pi  \over 16} + {{k\pi } \over 2},x = {{5\pi } \over {16}} + {{k\pi } \over 2}\)

A. \(x = {{k\pi } \over 2}\)

B. \(x = {{k\pi } \over 3}\)

C. \(x = {{k\pi } \over 4}\)

D. \(x = {{k\pi } \over 5}\)

A. \(x =  \pm {{2\pi } \over 5} + k\pi ,x = 2k\pi ,x = {\pi  \over 2} + k\pi \)

B. \(x =  \pm {{2\pi } \over 3} + 2k\pi ,x = 2k\pi ,x = {\pi  \over 2} + 2k\pi \)

C. \(x =  \pm {{2\pi } \over 3} + k\pi ,x = 2k\pi ,x = {\pi  \over 2} + k\pi \)

D. \(x =  \pm {{2\pi } \over 3} + 2k\pi ,x = 2k\pi ,x = {\pi  \over 2} + k\pi \)

A. \(x =   {\pi  \over {12}} + k2\pi ,x = {{7\pi } \over {12}} + k2\pi \)

B. \(x =  - {\pi  \over {12}} + k2\pi ,x = {{7\pi } \over {12}} + k2\pi \)

C. \(x =  - {\pi  \over {12}} + k\pi ,x = {{7\pi } \over {12}} + k\pi \)

D. \(x =  {\pi  \over {12}} + k\pi ,x = {{7\pi } \over {12}} + k\pi \)

A. \(x = k\pi ,x = {\pi  \over 2} + k\pi \)

B. \(x = k\pi ,x = {\pi  \over 3} + 2k\pi \)

C. \(x = k2\pi ,x = {\pi  \over 2} + 2k\pi \)

D. \(x = k\pi ,x = {\pi  \over 2} + 2k\pi \)

A. \(x = \pi  + k\pi ,\) \(x = {\pi  \over 6} + k\pi ,x = {{5\pi } \over 6} + k\pi \)

B. \(x = \pi  + k\pi ,\) \(x = {\pi  \over 6} + k2\pi ,x = {{5\pi } \over 6} + k\pi \)

C. \(x = \pi  + k\pi ,\) \(x = {\pi  \over 6} + k2\pi ,x = {{5\pi } \over 6} + k2\pi \)

D. \(x = \pi  + k2\pi ,\) \(x = {\pi  \over 6} + k2\pi ,x = {{5\pi } \over 6} + k2\pi \)

A. \(x = {\pi  \over 3} + k\pi ,x =  \pm {\pi  \over 6} + k\pi \)

B. \(x = {\pi  \over 2} + k\pi ,x =  \pm {\pi  \over 6} + k\pi \)

C. \(x = {\pi  \over 2} + k\pi ,x =  \pm {\pi  \over 6} + k2\pi \)

D. \(x = {\pi  \over 2} + k2\pi ,x =  \pm {\pi  \over 6} + k2\pi \)

A. \(x =  \pm {\pi  \over 2} + k2\pi \).

B. \(x =  \pm {\pi  \over 3} + k2\pi \).

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

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

A. \(x = {30^o} + k{180^o}\).

B. \(x = {90^o} + k{180^o}\).

C. \(x = {45^o} + k{360^o}\).

D. \(x = {45^o} + k{180^o}\).

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

B. \(x = k2\pi ,x = {\pi  \over 4} + k\pi \).

C. \(x = k\pi ,x = {\pi  \over 4} + k2\pi \).

D. \(x = k2\pi ,x = {\pi  \over 4} + k2\pi \).

A. \(\Leftrightarrow \left[ \begin{array}{l} x = \frac{\pi }{2} + k2\pi \\ x = \pm \frac{1}{2}\arccos \frac{1}{3} + k2\pi \end{array} \right.\)

B. \(\Leftrightarrow \left[ \begin{array}{l} x = \frac{\pi }{2} + k\pi \\ x = \pm \frac{1}{2}\arccos \frac{1}{3} + k2\pi \end{array} \right.\)

C. \(\Leftrightarrow \left[ \begin{array}{l} x = \frac{\pi }{2} + k2\pi \\ x = \pm \frac{1}{2}\arccos \frac{1}{3} + k\pi \end{array} \right.\)

D. \(\Leftrightarrow \left[ \begin{array}{l} x = \frac{\pi }{2} + k\pi \\ x = \pm \frac{1}{2}\arccos \frac{1}{3} + k\pi \end{array} \right.\)

A. \(x = {{k\pi } \over 2}\)

B. \(x = {{k\pi } \over 3}\)

C. \(x = {{k\pi } \over 4}\)

D. \(x = {{k\pi } \over 5}\)

A. \(x =  \pm {\pi  \over 3} + k2\pi \)

B. \(x =  \pm {\pi  \over 4} + k\pi \)

C. \(x =  \pm {\pi  \over 3} + k\pi \)

D. \(x =  \pm {\pi  \over 4} + k2\pi \)

A. \(x = {\pi  \over {16}} + {{k\pi } \over 4},x =  \pm {\pi  \over 3} + k\pi \)

B. \(x = {\pi  \over {16}} + {{k\pi } \over 8},x =  \pm {\pi  \over 3} + k2\pi \)

C. \(x = {\pi  \over {16}} + {{k\pi } \over 8},x =  \pm {\pi  \over 3} + k\pi \)

D. \(x = {\pi  \over {16}} + {{k\pi } \over 4},x =  \pm {\pi  \over 3} + k2\pi \)

A. \(x = {\pi  \over 2} + k2\pi ,x = {\pi  \over 4} + {{k\pi } \over 2},\) \(x = {\pi  \over {10}} + {{k\pi } \over 5}\)

B. \(x = {\pi  \over 2} + k\pi ,x = {\pi  \over 4} + {{k\pi } \over 2},\) \(x = {\pi  \over {10}} + {{k\pi } \over 4}\)

C. \(x = {\pi  \over 2} + k\pi ,x = {\pi  \over 4} + {{k\pi } \over 2},\) \(x = {\pi  \over {10}} + {{k\pi } \over 5}\)

D. \(x = {\pi  \over 3} + k\pi ,x = {\pi  \over 4} + {{k\pi } \over 2},\) \(x = {\pi  \over {10}} + {{k\pi } \over 5}\)

A. \(x = {{k\pi } \over 3},x =  \pm {\pi  \over {12}} + {{k\pi } \over 2}\).

B. \(x = {{k\pi } \over 4},x =  \pm {\pi  \over {12}} + {{k\pi } \over 3}\).

C. \(x = {{k\pi } \over 4},x =  \pm {\pi  \over {12}} + {{k\pi } \over 2}\).

D. \(x = {{k\pi } \over 3},x =  \pm {\pi  \over {12}} + {{k\pi } \over 3}\).

A. \(x = {{k\pi } \over 3};x = {{k\pi } \over 9}\).

B. \(x = {{k\pi } \over 2};x = {{k\pi } \over 9}\).

C. \(x = {{k\pi } \over 2};x = {{k\pi } \over 7}\).

D. \(x = {{k\pi } \over 3};x = {{k\pi } \over 7}\).

A. \(x = {\pi  \over 8} + {{k\pi } \over 4},x =  \pm {\pi  \over 4} + k\pi \).

B. \(x = {\pi  \over 8} + {{k\pi } \over 2},x =  \pm {\pi  \over 3} + k\pi \).

C. \(x = {\pi  \over 4} + {{k\pi } \over 4},x =  \pm {\pi  \over 3} + k\pi \).

D. \(x = {\pi  \over 8} + {{k\pi } \over 4},x =  \pm {\pi  \over 3} + k\pi \).

A. \(\Leftrightarrow \left[ \matrix{ x = {\pi \over {32}} + k{\pi \over {6}} \hfill \cr x = {\pi \over 4} + k{\pi \over 2} \hfill \cr} \right.\)

B. \(\Leftrightarrow \left[ \matrix{ x = {\pi \over {2}} + k{\pi \over {16}} \hfill \cr x = {\pi \over 4} + k{\pi \over 2} \hfill \cr} \right.\)

C. \(\Leftrightarrow \left[ \matrix{ x = {\pi \over {32}} + k{\pi \over {16}} \hfill \cr x = {\pi \over 4} + k{\pi \over 2} \hfill \cr} \right.\)

D. \(\Leftrightarrow \left[ \matrix{ x = {-\pi \over {32}} + k{\pi \over {16}} \hfill \cr x = {\pi \over 4} + k{\pi \over 2} \hfill \cr} \right.\)

A. \(x =  \pm {{2\pi } \over 3} + k2\pi ,x = k{\pi  \over 2}\)

B. \(x =  \pm {{\pi } \over 3} + k2\pi ,x = k{\pi  \over 2}\)

C. \(x =  \pm {{2\pi } \over 5} + k2\pi ,x = k{\pi  \over 2}\)

D. \(x =  \pm {{2\pi } \over 3} + k2\pi ,x = 3k{\pi  \over 2}\)

A. \(x = {{k\pi } \over 3},x =  \pm {\pi  \over 3} + k2\pi \)

B. \(x = {{k\pi } \over 4},x =  \pm {\pi  \over 3} + k2\pi \)

C. \(x = {{k\pi } \over 2},x =  \pm {\pi  \over 3} + k2\pi \)

D. \(x = {{k\pi } \over 4},x =  \pm {\pi  \over 3} + k\pi \)

A. \(\Leftrightarrow \left[ \begin{array}{l} x = \frac{{k\pi }}{4}\\ x = \frac{{k\pi }}{3}\\ x = \frac{\pi }{2} + k2\pi \end{array} \right.\)

B. \(\Leftrightarrow \left[ \begin{array}{l} x = \frac{{k\pi }}{5}\\ x = \frac{{k\pi }}{3}\\ x = \frac{\pi }{2} + k2\pi \end{array} \right.\)

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

D. \(\Leftrightarrow \left[ \begin{array}{l} x = \frac{{k\pi }}{5}\\ x = \frac{{k\pi }}{3}\\ x = \frac{\pi }{2} + k\pi \end{array} \right.\)

A. \(x = {\pi  \over 2} - k\pi ;x = {\pi  \over {18}} + {{k\pi } \over 9}\)

B. \(x = {\pi  \over 2} + k\pi ;x = {\pi  \over {18}} + {{k\pi } \over 9}\)

C. \(x = {\pi  \over 2} + k\pi ;x = {\pi  \over {8}} + {{k\pi } \over 9}\)

D. \(x = {\pi  \over 2} + k\pi ;x = {\pi  \over {18}} + {{k\pi } \over 3}\)

A. \(x = {{k\pi } \over 4},x = {\pi  \over {24}} + {{k\pi } \over {12}}\).

B. \(x = {{k\pi } \over 4},x = {\pi  \over {12}} + {{k\pi } \over {12}}\).

C. \(x = {{k\pi } \over 2},x = {\pi  \over {24}} + {{k\pi } \over {12}}\).

D. \(x = {{k\pi } \over 3},x = {\pi  \over {24}} + {{k\pi } \over {12}}\).

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

B. \(x = {{k\pi } \over 3}\).

C. \(x = {{k\pi } \over 4}\).

D. \(x = {{k3\pi } \over 4}\).

A. \(x =  - {\pi  \over 4} + 2k\pi \) và \(x =  \pm {\pi  \over 3} + 2k\pi \).

B. \(x =   {\pi  \over 2} + 2k\pi \) và \(x =  \pm {\pi  \over 3} + 2k\pi \).

C. \(x =  - {\pi  \over 2} + k\pi \) và \(x =  \pm {\pi  \over 3} + k\pi \).

D. \(x =  - {\pi  \over 2} + 2k\pi \) và \(x =  \pm {\pi  \over 3} + 2k\pi \).

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

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

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

D. \(x = \frac{\pi }{3} + k2\pi\)

A. \(x = \dfrac{\pi }{4} + k\pi ,x = \arctan \dfrac{1}{3} + k\pi \).

B. \(x = \dfrac{\pi }{3} + k\pi ,x = \arctan \dfrac{1}{3} + k\pi \).

C. \(x = \dfrac{\pi }{4} + k2\pi ,x = \arctan \dfrac{1}{3} + k2\pi \).

D. \(x = \dfrac{\pi }{3} + k2\pi ,x = \arctan \dfrac{1}{3} + k2\pi \).

A. \(x = \dfrac{\pi }{4} + \dfrac{{k\pi }}{2},\) \(x = \dfrac{1}{2}{\mathop{\rm arccot}\nolimits} \left( { - 3} \right) + \dfrac{{k\pi }}{2}\).

B. \(x = \dfrac{\pi }{4} + \dfrac{{k\pi }}{3},\) \(x = \dfrac{1}{2}{\mathop{\rm arccot}\nolimits} \left( { - 3} \right) + \dfrac{{k\pi }}{2}\).

C. \(x = \dfrac{\pi }{4} + \dfrac{{k\pi }}{2},\) \(x = \dfrac{1}{2}{\mathop{\rm arccot}\nolimits} \left( { - 3} \right) + \dfrac{{k\pi }}{3}\).

D. \(x = \dfrac{\pi }{4} + \dfrac{{k\pi }}{3},\) \(x = \dfrac{1}{2}{\mathop{\rm arccot}\nolimits} \left( { - 3} \right) + \dfrac{{k\pi }}{3}\).

A. \(x = \dfrac{\pi }{3} + k\pi ,x = \dfrac{\pi }{2} + k\pi \).

B. \(x = \dfrac{\pi }{4} + k\pi ,x = \dfrac{\pi }{3} + k\pi \).

C. \(x = \dfrac{\pi }{4} + k\pi ,x = \dfrac{\pi }{2} + k\pi \).

D. \(x = \dfrac{\pi }{4} + k2\pi ,x = \dfrac{\pi }{2} + k2\pi \).

A. \(x =  \dfrac{\pi }{4} + k\pi \) và \(x = \arctan \left( {\dfrac{3}{4}} \right) + k\pi \).

B. \(x =  - \dfrac{\pi }{4} + k\pi \) và \(x = \arctan \left( {\dfrac{3}{4}} \right) + k\pi \).

C. \(x =  - \dfrac{\pi }{4} + k\pi \) và \(x = \arctan \left( {\dfrac{1}{4}} \right) + k\pi \).

D. \(x =  - \dfrac{\pi }{4} + k2\pi \) và \(x = \arctan \left( {\dfrac{3}{4}} \right) + k2\pi \).

A. \(x =  - \dfrac{\pi }{4} + k2\pi \) và \(x = \arctan 3 + k2\pi \).

B. \(x =   \dfrac{\pi }{4} + k\pi \) và \(x = \arctan 3 + k\pi \).

C. \(x =  - \dfrac{\pi }{4} + k\pi \) và \(x = \arctan 3 + k\pi \).

D. \(x =  - \dfrac{\pi }{3} + k\pi \) và \(x = \arctan 3 + k\pi \).

A. Với mọi \(\alpha \)

B. Không có \(\alpha \)

C. \(\alpha = \pi\)

D. \(\alpha = 2\pi\)

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

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

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

D. \(\alpha = \frac{\pi }{4} + k2\pi\)

A. \(x = {\pi  \over 2}\)

B. \(x = {\pi  \over 3}\)

C. \(x = {\pi  \over 4}\)

D. \(x = {\pi  \over 5}\)