Bài tập 17 trang 200 SGK Toán 10 NC

a) Ta có 

\( - \frac{\pi }{3} + \left( {2k + 1} \right)\pi  = \frac{{2\pi }}{3} + k2\pi \)

\(\begin{array}{l}
\sin \left( {\frac{{2\pi }}{3} + k2\pi } \right) = \sin \frac{{2\pi }}{3} = \frac{{\sqrt 3 }}{2}\\
{\rm{cos}}\left( {\frac{{2\pi }}{3} + k2\pi } \right) = {\rm{cos}}\frac{{2\pi }}{3} =  - \frac{1}{2}\\
\tan \left( {\frac{{2\pi }}{3} + k2\pi } \right) = \tan \frac{{2\pi }}{3} =  - \sqrt 3 \\
\cot \left( {\frac{{2\pi }}{3} + k2\pi } \right) = \cot \frac{{2\pi }}{3} =  - \frac{{\sqrt 3 }}{3}
\end{array}\)

b) Ta có

\(\cos k\pi  = {\left( { - 1} \right)^k};\sin k\pi  = 0\)

\(\tan k\pi  = 0,\cot k\pi \) không xác định \(\left( {k \in Z} \right)\)

c) Ta có 

\({\rm{cos}}\left( {\frac{\pi }{2} + k\pi } \right) = 0;\sin \left( {\frac{\pi }{2} + k\pi } \right) = {\left( { - 1} \right)^k};\)

\(\cot \left( {\frac{\pi }{2} + k\pi } \right) = 0;\tan \left( {\frac{\pi }{2} + k\pi } \right)\) không xác định \(\left( {k \in Z} \right)\)

d)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
{\rm{cos}}\left( {\frac{\pi }{4} + k\pi } \right) = {\left( { - 1} \right)^k}.\frac{{\sqrt 2 }}{2};\\
\sin \left( {\frac{\pi }{4} + k\pi } \right) = {\left( { - 1} \right)^k}.\frac{{\sqrt 2 }}{2}
\end{array}\\
{\tan \left( {\frac{\pi }{4} + k\pi } \right) = \cot \left( {\frac{\pi }{4} + k\pi } \right) = 1}
\end{array}\)

-- Mod Toán 10 HỌC247