Bài tập 16 trang 200 SGK Toán 10 NC

Bài tập 16 trang 200 SGK Toán 10 NC

a) Vì 0⁰ < 156⁰ < 180⁰ nên sin 156⁰ > 0

Vì - 90⁰ < - 80⁰ < 90⁰ nên cos(- 80⁰) > 0

Ta có

\(\begin{array}{l}
\tan \left( { - \frac{{17\pi }}{8}} \right) = \tan \left( { - 2\pi  - \frac{\pi }{8}} \right)\\
 = \tan \left( { - \frac{\pi }{8}} \right) < 0
\end{array}\)

(vì \( - \frac{\pi }{2} <  - \frac{\pi }{8} < 0\))

\(\begin{array}{l}
\tan {556^0} = \tan \left( {{{360}^0} + {{196}^0}} \right)\\
 = \tan {196^0} > 0
\end{array}\)

(vì \({180^0} < {156^0} < {270^0}\))

b) Ta có:

\(\begin{array}{*{20}{l}}
\begin{array}{l}
0 < \alpha  < \frac{\pi }{2}\\
 \Rightarrow \frac{\pi }{4} < \alpha  + \frac{\pi }{4} < \frac{{3\pi }}{4}\\
 \Rightarrow \sin \left( {\alpha  + \frac{\pi }{4}} \right) > 0
\end{array}\\
\begin{array}{l}
0 < \alpha  < \frac{\pi }{2}\\
 \Rightarrow  - \frac{{3\pi }}{8} < \alpha  - \frac{{3\pi }}{8} < \frac{\pi }{8}\\
 \Rightarrow \cos \left( {\alpha  - \frac{{3\pi }}{8}} \right) > 0
\end{array}\\
\begin{array}{l}
0 < \alpha  < \frac{\pi }{2}\\
 \Rightarrow  - \frac{\pi }{2} < \alpha  - \frac{\pi }{2} < 0\\
 \Rightarrow \tan \left( {\alpha  - \frac{\pi }{2}} \right) < 0
\end{array}
\end{array}\)

-- Mod Toán 10