Синус и косинус угла. Задача 10math100admin44242025-03-21T17:21:18+03:00
Задача 10. Вычислите \(\dfrac{{\sqrt {12} }}{5}\left( {\sin \dfrac{{19\pi }}{3} + \cos \dfrac{{23\pi }}{6}} \right)\)
Решение
\(\dfrac{{\sqrt {12} }}{5}\left( {\sin \dfrac{{19\pi }}{3} + \cos \dfrac{{23\pi }}{6}} \right) = \dfrac{{\sqrt {12} }}{5} \cdot \left( {\sin \left( {\dfrac{{19\pi }}{3}-6\pi } \right) + \cos \left( {\dfrac{{23\pi }}{6}-4\pi } \right)} \right) = \)
\( = \dfrac{{\sqrt {12} }}{5}\left( {\sin \dfrac{\pi }{3} + \cos \left( {-\dfrac{\pi }{6}} \right)} \right) = \dfrac{{\sqrt {12} }}{5} \cdot \left( {\dfrac{{\sqrt 3 }}{2} + \dfrac{{\sqrt 3 }}{2}} \right) = \dfrac{{\sqrt {12} \cdot \sqrt 3 }}{5} = 1,2.\)
Ответ: 1,2.