Đáp án:
\(\begin{array}{l}
\cos a = \frac{3}{5}\\
\sin \left( {a - \frac{\pi }{4}} \right) = - \frac{{7\sqrt 2 }}{{10}}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
{\sin ^2}a + {\cos ^2}a = 1\\
\to {\left( { - 0,8} \right)^2} + {\cos ^2}a = 1\\
\to {\cos ^2}a = \frac{9}{{25}}\\
Do:a \in \left( {\frac{{3\pi }}{2};2\pi } \right)\\
\to \cos a > 0\\
\to \cos a = \frac{3}{5}\\
\sin \left( {a - \frac{\pi }{4}} \right) = \sin a.\cos \frac{\pi }{4} - \cos a.\sin \frac{\pi }{4}\\
= - \frac{4}{5}.\frac{{\sqrt 2 }}{2} - \frac{3}{5}.\frac{{\sqrt 2 }}{2} = - \frac{{7\sqrt 2 }}{{10}}
\end{array}\)
