Odpowiedź:
[tex] \tg \alpha = 4 \\ \frac{ \sin \alpha }{ \cos \alpha } =4\\ \sin \alpha = 4 \cos \alpha \\ \\ \ctg \alpha = \frac{1}{tg \alpha } = \frac{1}{4} \\ \\ \\ {sin}^{2} \alpha + {cos}^{2} \alpha = 1 \\ (4cos \alpha {)}^{2} + {cos}^{2} \alpha = 1 \\ 16 {cos}^{2} \alpha + {cos}^{2} \alpha = 1 \\ 17 {cos}^{2} \alpha = 1 \\ {cos}^{2} \alpha = \frac{1}{17} \\ \cos \alpha = \sqrt{ \frac{1}{17} } = \frac{1}{ \sqrt{17} } = \frac{ \sqrt{17} }{17} \\ \\ \sin \alpha = 4 \cos \alpha = 4 \times \frac{ \sqrt{17} }{17} = \frac{4 \sqrt{17} }{17} [/tex]
