The sine function is the ratio between the opposite leg and the hypothenuse
![\sin \theta=\frac{3}{\sqrt[]{13}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/cb2cg37jnb0h6iq41dwm9linpi1hcyi0nk.png)
Then, we rationalize.
![\sin \theta=\frac{3}{\sqrt[]{13}}\cdot\frac{\sqrt[]{13}}{\sqrt[]{13}}=\frac{3\sqrt[]{13}}{13}](https://img.qammunity.org/2023/formulas/mathematics/high-school/rxc1i9r454hn7y4ixd0dsh9srbnxm6i699.png)
The cosine function is the ratio between the adjacent leg and the hypothenuse.
![\begin{gathered} cos\theta=\frac{2}{\sqrt[]{13}} \\ \cos \theta=\frac{2}{\sqrt[]{13}}\cdot\frac{\sqrt[]{13}}{\sqrt[]{13}}=\frac{2\sqrt[]{13}}{13} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/4vnrpgwn1p4q9gphnfezztx7s1omr4vn1l.png)
At last, the tangent function is the ratio between the opposite leg and the adjacent leg.
