0\; ,\; \; tga>0\; ,\; \; ctga>0\\\\\\\boxed {\; sin^2a+cos^2a=1\; }\; \; \; \Rightarrow \; \; \; cos^2a=1-sin^2a\; ,\; \; cosa=\pm \sqrt{1-sin^2a}\\\\\\cosa>0\; \; \to \; \; \; cosa=+\sqrt{1-sin^2a}=\sqrt{1-\dfrac{9}{13}}=\sqrt{\dfrac{4}{13}}=\dfrac{2}{\sqrt{13}}\\\\\\tga=\dfrac{sina}{cosa}=\dfrac{\frac{3}{\sqrt{13}}}{\frac{2}{\sqrt{13}}}=\dfrac{3}{2}\\\\\\ctga=\dfrac{1}{tga}=\dfrac{2}{3}" alt="sina=\dfrac{3}{\sqrt{13}}\\\\a\in (0^\circ ;90^\circ )\; \; \Rightarrow \; \; \; cosa>0\; ,\; \; tga>0\; ,\; \; ctga>0\\\\\\\boxed {\; sin^2a+cos^2a=1\; }\; \; \; \Rightarrow \; \; \; cos^2a=1-sin^2a\; ,\; \; cosa=\pm \sqrt{1-sin^2a}\\\\\\cosa>0\; \; \to \; \; \; cosa=+\sqrt{1-sin^2a}=\sqrt{1-\dfrac{9}{13}}=\sqrt{\dfrac{4}{13}}=\dfrac{2}{\sqrt{13}}\\\\\\tga=\dfrac{sina}{cosa}=\dfrac{\frac{3}{\sqrt{13}}}{\frac{2}{\sqrt{13}}}=\dfrac{3}{2}\\\\\\ctga=\dfrac{1}{tga}=\dfrac{2}{3}" align="absmiddle" class="latex-formula">