Dany jest cosα oraz wiemy , że α- to kąt ostry. Najpierw obliczę sinus korzystając z jedynki trygonometrycznej, a potem pozostałe wartości funkcji trygonometrycznych.
[tex]sin^{2} \alpha +cos^{2} \alpha =1~~\land~~cos\alpha =\dfrac{3}{5} \\\\sin^{2} \alpha +( \dfrac{3}{5} )^{2} =1\\\\sin^{2} \alpha +\dfrac{9}{25} =1\\\\sin^{2} \alpha =1-\dfrac{9}{25}\\\\sin^{2} \alpha=\dfrac{16}{25}~~\land ~~~~\alpha -~~kat~~ostry\\\\sin\alpha =\dfrac{4}{5} \\\\\\[/tex]
[tex]tg\alpha =\dfrac{sin\alpha }{cos\alpha } ~~\land~~cos\alpha =\dfrac{3}{5} ~~\land~~sin\alpha =\dfrac{4}{5} \\\\\\tg\alpha =\dfrac{4}{5} \div \dfrac{3}{5} \\\\\\tg\alpha =\dfrac{4}{5} \cdot \dfrac{5}{3} \\\\tg\alpha =\dfrac{4}{3} \\\\tg\alpha =1\frac{1}{3} \\\\\\\\ctg\alpha =\dfrac{cos\alpha }{sin\alpha } ~~~\lor ~~ctg\alpha =\dfrac{1}{tg\alpha } \\\\ctg\alpha =\dfrac{1}{tg\alpha }~~\land ~~tg\alpha =\dfrac{4}{3} ~~\Rightarrow ~~ctg\alpha =\dfrac{3}{4}[/tex]
