588. Найдите \(\cos \beta\), \(\tan \beta\) и \(\cot \beta\), если \(\sin \beta = \frac{4}{5}\).

Решение: 1. Найдем \(\cos \beta\) используя основное тригонометрическое тождество: \(\sin^2 \beta + \cos^2 \beta = 1\) \(\cos^2 \beta = 1 - \sin^2 \beta = 1 - (\frac{4}{5})^2 = 1 - \frac{16}{25} = \frac{9}{25}\) \(\cos \beta = \sqrt{\frac{9}{25}} = \frac{3}{5}\) 2. Найдем \(\tan \beta\): \(\tan \beta = \frac{\sin \beta}{\cos \beta} = \frac{\frac{4}{5}}{\frac{3}{5}} = \frac{4}{3}\) 3. Найдем \(\cot \beta\): \(\cot \beta = \frac{1}{\tan \beta} = \frac{1}{\frac{4}{3}} = \frac{3}{4}\) Ответ: \(\cos \beta = \frac{3}{5}\), \(\tan \beta = \frac{4}{3}\), \(\cot \beta = \frac{3}{4}\)