Đề kiểm tra 1 tiết chương 1: Hàm số lượng giác và phương trình lượng giác - Đề số 1

$\left[ \begin{array}{l}x = \dfrac{\pi }{3} + k2\pi \\x = \dfrac{\pi }{6} + k2\pi \end{array} \right.\,\,\left( {k \in Z} \right)$

$\left[ \begin{array}{l}x =  - \dfrac{\pi }{3} + k\pi \\x =  - \dfrac{\pi }{6} + k\pi \end{array} \right.\,\,\left( {k \in Z} \right)$

$\left[ \begin{array}{l}x =  - \dfrac{\pi }{3} + k2\pi \\x = \dfrac{\pi }{6} + k\pi \end{array} \right.\,\,\left( {k \in Z} \right)$

\(x = \dfrac{\pi }{8} + k\pi \left( {k \in Z} \right)\)

\(x = \dfrac{\pi }{8} + \dfrac{{k\pi }}{4}\left( {k \in Z} \right)\)

\(x = \dfrac{\pi }{8} + \dfrac{{k\pi }}{2}\left( {k \in Z} \right)\)

\(1\)     

\(0\)      

\(3\)

\(M\left( {0;1} \right)\)

\(N\left( {\dfrac{\pi }{2};0} \right)\)

\(P\left( {1;0} \right)\)

\(m = 1\)

Không có m

\(m = 0\)

\( - \dfrac{{5{\pi ^2}}}{{12}}\)           

\(\dfrac{{5{\pi ^2}}}{{144}}\)

\(\dfrac{{{\pi ^2}}}{{12}}\) 

\(D = \mathbb{R}\backslash \left\{ { - \dfrac{\pi }{8} + k\dfrac{\pi }{4},k \in \mathbb{Z}} \right\}\)

\(D = \mathbb{R}\backslash \left\{ { - \dfrac{{3\pi }}{8} + k\dfrac{\pi }{2},k \in \mathbb{Z}} \right\}\) 

\(D = \mathbb{R}\backslash \left\{ {\dfrac{{k2\pi }}{3},k \in \mathbb{Z}} \right\}\)

\(x = \dfrac{{5\pi }}{6} + k2\pi\)

\(x = \dfrac{{5\pi }}{6}\)

\(x = \dfrac{\pi }{3}\)

\(\max y = 4;\min y = \dfrac{3}{4}\)

\(\max y = 3;\min y = 2\)

\(\max y = 4;\min y = 2\)

\(x = \dfrac{\pi }{4} + k\pi \left( {k \in Z} \right)\)

\(x = \dfrac{\pi }{4} + \dfrac{{k\pi }}{2}\left( {k \in Z} \right)\)

\(x = \dfrac{{3\pi }}{4} + 2k\pi \left( {k \in Z} \right)\)        

\(\sin x =  - 1 \Leftrightarrow x =  - \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)\)           

\(\sin x = 0 \Leftrightarrow x = k\pi \left( {k \in Z} \right)\)

\(\sin x = 1 \Leftrightarrow x = \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)\) 

\(x = \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)\)

\(x = k2\pi \left( {k \in Z} \right)\)

\(x = \dfrac{\pi }{2} + k\pi \left( {k \in Z} \right)\)

\(y = \tan x\)

\(y = \cot x\)

\(y = \sin x\)     

\(x = \dfrac{\pi }{3} + k\pi \left( {k \in Z} \right)\)

\(x =  - \dfrac{\pi }{3} + k2\pi \left( {k \in Z} \right)\)          

\(x = \dfrac{\pi }{6} + k\pi \left( {k \in Z} \right)\)

$0$     

$1$     

$4$

\(\min y =  - 5;\max y = 5\)

\(\min y =  - 3;\max y = 4\)      

\(\min y =  - 6;\max y = 6\)

\(\max y = \sqrt 5 ,\min y = 0\)

\(\max y = \sqrt 5 ,\min y = \sqrt 3 \)

\(\max y = \sqrt 5 ,\min y = 3\) 

\(x = k2\pi ,x = \dfrac{\pi }{2} + k2\pi \left( {k \in Z} \right)\)

\(x = k\pi ,x = \dfrac{\pi }{4} + k\pi \left( {k \in Z} \right)\)

\(x = \dfrac{\pi }{8} + \dfrac{{k\pi }}{2},x =  - \dfrac{\pi }{4} + k\pi \left( {k \in Z} \right)\)

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

\(\left[ \begin{array}{l}x = \dfrac{\pi }{8} + k2\pi \\x = \dfrac{\pi }{{12}} + k2\pi \end{array} \right.\,\,\left( {k \in Z} \right)\)          

\(\left[ \begin{array}{l}x = \dfrac{\pi }{8} + k\pi \\x = \dfrac{\pi }{{12}} + k\pi \end{array} \right.\,\,\left( {k \in Z} \right)\)          

$0$

$1$     

$3$

\(x = k\pi \,\,\left( {k \in \mathbb{Z}} \right)\)         

\(x = \dfrac{\pi }{6} + k2\pi \,\,\left( {k \in \mathbb{Z}} \right)\)    

Tất cả đều đúng.

\(\left| a \right| \ge 1\)

\(\left| a \right| = 1\)

\(\left| a \right| \ne 1\)

Ba nghiệm      

Một nghiệm     

Hai nghiệm

\(\left\{ \begin{array}{l}x = \dfrac{\pi }{6} + k2\pi \\y =  - \dfrac{\pi }{6} + k2\pi \end{array} \right.\left( {k \in Z} \right)\)          

\(\left\{ \begin{array}{l}x = \dfrac{{2\pi }}{3} + k2\pi \\y = \dfrac{\pi }{3} - k2\pi \end{array} \right.\left( {k \in Z} \right)\)                      

\(\left\{ \begin{array}{l}x = \dfrac{\pi }{2} + k2\pi \\y = \dfrac{\pi }{6} + k2\pi \end{array} \right.\left( {k \in Z} \right)\)

\(\max y = 2 + \sqrt 5 ;\min y = 2 - \sqrt 5 \)

\(\max y = 2 + \sqrt 2 ;\min y = 2 - \sqrt 2 \)

\(\max y = 2 + \sqrt 7 ;\min y = 2 - \sqrt 7 \)