3. Вычислите sin(9π/4) - cos(11π/4) : sin(-3.5π) : cos(-28π/3)

Сначала упростим каждый тригонометрический аргумент: \(\sin(\frac{9\pi}{4}) = \sin(\frac{9\pi}{4} - 2\pi) = \sin(\frac{9\pi - 8\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}\) \(\cos(\frac{11\pi}{4}) = \cos(\frac{11\pi}{4} - 2\pi) = \cos(\frac{11\pi - 8\pi}{4}) = \cos(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2}\) \(\sin(-3.5\pi) = \sin(-3.5\pi + 4\pi) = \sin(0.5\pi) = \sin(\frac{\pi}{2}) = 1\) \(\cos(-\frac{28\pi}{3}) = \cos(-\frac{28\pi}{3} + 10\pi) = \cos(-\frac{28\pi}{3} + \frac{30\pi}{3}) = \cos(\frac{2\pi}{3}) = -\frac{1}{2}\) Теперь подставим значения в исходное выражение: \(\frac{\sqrt{2}}{2} - \left(-\frac{\sqrt{2}}{2}\right) : 1 : \left(-\frac{1}{2}\right) = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} : 1 : \left(-\frac{1}{2}\right) = \sqrt{2} : 1 : \left(-\frac{1}{2}\right) = \sqrt{2} : \left(-\frac{1}{2}\right) = -2\sqrt{2}\) Ответ: \(-2\sqrt{2}\)