Задание 10. Найдите sina, если... 1) ... cosa = 26, a∈(0;) 2)... cosa, a∈ (0;) 3)... cosa =, αㅌ(;) √21 αε 4) ... cosa=-21, α∈(;) Задание 11. 5 * 1) Найдите Эcos2а, если sina=0,6 2) Найдите 16cos2а, если cosa=0,5 3) Найдите 4cos2а, если sina=-0,5 4) Найдите 3cos2a, если cosa=-0,8 5)... cosa=-, α€ (π; 3) 6) ... cosa=-15, α€ (π;3) 7) ... cosa = 1, αε (3; 2π) απ 2π 8)... cosa, αε (3:27)

Задание 10:

1. cosα = \(\frac{2\sqrt{6}}{5}\), \(α ∈ (0; \frac{π}{2})\)

   sin²α = 1 - cos²α = 1 - \(\frac{24}{25}\) = \(\frac{1}{25}\)

   sinα = \(\sqrt{\frac{1}{25}}\) = \(\frac{1}{5}\) (т.к. \(α ∈ (0; \frac{π}{2})\), sinα > 0)

2. cosα = \(\frac{\sqrt{19}}{10}\), \(α ∈ (0; \frac{π}{2})\)

   sin²α = 1 - cos²α = 1 - \(\frac{19}{100}\) = \(\frac{81}{100}\)

   sinα = \(\sqrt{\frac{81}{100}}\) = \(\frac{9}{10}\) (т.к. \(α ∈ (0; \frac{π}{2})\), sinα > 0)

3. cosα = -\(\frac{\sqrt{7}}{4}\), \(α ∈ (\frac{π}{2}; π)\)

   sin²α = 1 - cos²α = 1 - \(\frac{7}{16}\) = \(\frac{9}{16}\)

   sinα = \(\sqrt{\frac{9}{16}}\) = \(\frac{3}{4}\) (т.к. \(α ∈ (\frac{π}{2}; π)\), sinα > 0)

4. cosα = -\(\frac{\sqrt{21}}{5}\), \(α ∈ (\frac{π}{2}; π)\)

   sin²α = 1 - cos²α = 1 - \(\frac{21}{25}\) = \(\frac{4}{25}\)

   sinα = \(\sqrt{\frac{4}{25}}\) = \(\frac{2}{5}\) (т.к. \(α ∈ (\frac{π}{2}; π)\), sinα > 0)

5. cosα = -\(\frac{\sqrt{19}}{10}\), \(α ∈ (π; \frac{3π}{2})\)

   sin²α = 1 - cos²α = 1 - \(\frac{19}{100}\) = \(\frac{81}{100}\)

   sinα = -\(\sqrt{\frac{81}{100}}\) = -\(\frac{9}{10}\) (т.к. \(α ∈ (π; \frac{3π}{2})\), sinα < 0)

6. cosα = -\(\frac{\sqrt{51}}{10}\), \(α ∈ (π; \frac{3π}{2})\)

   sin²α = 1 - cos²α = 1 - \(\frac{51}{100}\) = \(\frac{49}{100}\)

   sinα = -\(\sqrt{\frac{49}{100}}\) = -\(\frac{7}{10}\) (т.к. \(α ∈ (π; \frac{3π}{2})\), sinα < 0)

7. cosα = \(\frac{\sqrt{91}}{10}\), \(α ∈ (\frac{3π}{2}; 2π)\)

   sin²α = 1 - cos²α = 1 - \(\frac{91}{100}\) = \(\frac{9}{100}\)

   sinα = -\(\sqrt{\frac{9}{100}}\) = -\(\frac{3}{10}\) (т.к. \(α ∈ (\frac{3π}{2}; 2π)\), sinα < 0)

8. cosα = \(\frac{\sqrt{7}}{4}\), \(α ∈ (\frac{3π}{2}; 2π)\)

   sin²α = 1 - cos²α = 1 - \(\frac{7}{16}\) = \(\frac{9}{16}\)

   sinα = -\(\sqrt{\frac{9}{16}}\) = -\(\frac{3}{4}\) (т.к. \(α ∈ (\frac{3π}{2}; 2π)\), sinα < 0)

Задание 11:

1. Найдите 3cos2α, если sinα = 0,6

   cos2α = 1 - 2sin²α = 1 - 2(0,6)² = 1 - 2(0,36) = 1 - 0,72 = 0,28

   3cos2α = 3 \( \cdot \) 0,28 = 0,84

2. Найдите 16cos2α, если cosα = 0,5

   cos2α = 2cos²α - 1 = 2(0,5)² - 1 = 2(0,25) - 1 = 0,5 - 1 = -0,5

   16cos2α = 16 \( \cdot \) (-0,5) = -8

3. Найдите 4cos2α, если sinα = -0,5

   cos2α = 1 - 2sin²α = 1 - 2(-0,5)² = 1 - 2(0,25) = 1 - 0,5 = 0,5

   4cos2α = 4 \( \cdot \) 0,5 = 2

4. Найдите 3cos2α, если cosα = -0,8

   cos2α = 2cos²α - 1 = 2(-0,8)² - 1 = 2(0,64) - 1 = 1,28 - 1 = 0,28

   3cos2α = 3 \( \cdot \) 0,28 = 0,84