Hey there! I'm happy to help you!
When talking about trigonometric ratios, we can use a handy little mnemonic device called soh cah toa which shows us the ratios for each one. Soh is sine equals opposite over hypotenuse, cah is cosine equals adjacent over hypotenuse, and toa is tangent equals opposite over adjacent.
In our triangle, we can apply the following with the given information.
[tex]sin=\frac{opposite}{hypotenuse} =\frac{9}{3\sqrt{13} } =\frac{3}{\sqrt{13} } =\frac{3\sqrt{13} }{13} \\\\cos=\frac{adjacent}{hypotenuse} =\frac{6}{3\sqrt{13} } =\frac{2}{\sqrt{13} } =\frac{2\sqrt{13} }{13} \\\\tan=\frac{opposite}{adjacent} =\frac{6}{9} =\frac{2}{3}[/tex]
Therefore, the answers will be sin, cos, and then tan going down in the answer order you gave!
I hope that this helps! Have a wonderful day!
