[tex]\alpha -kat~~ostry\\korzystam~~z ~~jedynki~~trygonometrycznej~~by~~obliczyc~~cos\alpha :\\\\sin^{2} \alpha +cos^{2} \alpha =1~~\land~~sin\alpha =\dfrac{1}{4} \\\\(\dfrac{1}{4} } )^{2} +cos^{2} \alpha =1\\\\cos^{2} \alpha =1-\dfrac{1}{16} \\\\cos^{2} \alpha =\dfrac{15}{16} ~~\land~~\alpha -kat~~ostry~~\Rightarrow~~cos\alpha =\sqrt{\dfrac{15}{16} } \\\\cos\alpha =\sqrt{\dfrac{15}{16} }\\\\cos\alpha =\dfrac{\sqrt{15} }{\sqrt{16} } \\\\cos\alpha =\dfrac{\sqrt{15} }{\sqrt{4^{2} } } \\\\[/tex]
[tex]cos\alpha =\dfrac{\sqrt{15} }{4 } \\\\\\tg\alpha =\dfrac{sin\alpha }{cos\alpha } ~\land~~sin\alpha =\dfrac{1}{4} ~~\land~~cos\alpha =\dfrac{\sqrt{15} }{4 }\\\\\\tg\alpha =\dfrac{\dfrac{1}{4} }{\dfrac{\sqrt{15} }{4 } } \\\\\\tg\alpha =\dfrac{1}{4} \div \dfrac{\sqrt{15} }{4 }\\\\\\tg\alpha =\dfrac{1}{4} \cdot \dfrac{4 }{\sqrt{15} }\\\\\\tg\alpha =\dfrac{1}{\sqrt{15} }\cdot \dfrac{\sqrt{15} }{\sqrt{15} }\\\\\\tg\alpha =\dfrac{\sqrt{15} }{15 }[/tex]
