1. Вычислите: a) cos a n tga, ecли sin a = -0,8,3<a<2π; 24 Зл 6) sina utga, если cos a = -25, π<<; 24 π B) cosa, tga, ctga, если sin a=25, 2<α<π;

a) \( sin a = -0.8 \), \( \frac{3\pi}{2} < a < 2\pi \)

\[ cos^2 a = 1 - sin^2 a = 1 - (-0.8)^2 = 1 - 0.64 = 0.36 \]

Так как \( \frac{3\pi}{2} < a < 2\pi \), то \( cos a > 0 \), следовательно, \( cos a = \sqrt{0.36} = 0.6 \)

\[ tg a = \frac{sin a}{cos a} = \frac{-0.8}{0.6} = -\frac{4}{3} \]

Ответ: \( cos a = 0.6 \), \( tg a = -\frac{4}{3} \)

б) \( cos a = -\frac{24}{25} \), \( \pi < a < \frac{3\pi}{2} \)

\[ sin^2 a = 1 - cos^2 a = 1 - \left(-\frac{24}{25}\right)^2 = 1 - \frac{576}{625} = \frac{625 - 576}{625} = \frac{49}{625} \]

Так как \( \pi < a < \frac{3\pi}{2} \), то \( sin a < 0 \), следовательно, \( sin a = -\sqrt{\frac{49}{625}} = -\frac{7}{25} \)

\[ tg a = \frac{sin a}{cos a} = \frac{-\frac{7}{25}}{-\frac{24}{25}} = \frac{7}{24} \]

Ответ: \( sin a = -\frac{7}{25} \), \( tg a = \frac{7}{24} \)

в) \( sin a = \frac{24}{25} \), \( \frac{\pi}{2} < a < \pi \)

\[ cos^2 a = 1 - sin^2 a = 1 - \left(\frac{24}{25}\right)^2 = 1 - \frac{576}{625} = \frac{625 - 576}{625} = \frac{49}{625} \]

Так как \( \frac{\pi}{2} < a < \pi \), то \( cos a < 0 \), следовательно, \( cos a = -\sqrt{\frac{49}{625}} = -\frac{7}{25} \)

\[ tg a = \frac{sin a}{cos a} = \frac{\frac{24}{25}}{-\frac{7}{25}} = -\frac{24}{7} \]

\[ ctg a = \frac{1}{tg a} = -\frac{7}{24} \]

Ответ: \( cos a = -\frac{7}{25} \), \( tg a = -\frac{24}{7} \), \( ctg a = -\frac{7}{24} \)