найдите косинус а, если синус а = 5\6 и 0 < a < п/2.

найдите косинус а, если синус а = 5\6 и 0 < a < п/2.
- Предмет:
  Математика
- Автор:
  willieiefd
- 5 лет назад

Ответы 2

Основное тригонометрическое тождество:
$sin^2\alpha +cos^2\alpha =1\\ cos^2\alpha =1-sin^2\alpha \\ cos\alpha =\sqrt{1-sin^2\alpha } \\$
$cos\alpha= \sqrt{1-\frac{5}{6}^2 } =\sqrt{1-\frac{25}{36} } =\sqrt{\frac{11}{36} } =\frac{\sqrt{11} }{6}$
И так как угол от нуля до Пи/2, косинус должен быть положительным. Следовательно, оставляем его со знаком плюс.
- Автор:
  friendo
- 5 лет назад
- 0
Дана первая четверть. Поэтому cosα=√(1-sin²α)=√(√(1-25/36)=√11/6
- Автор:
  cirinopfko
- 5 лет назад
- 0
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найдите косинус а, если синус а = 5\6 и 0 < a < п/2.

Ответы 2

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