1. **Problem statement:** Find the exact expressions for the three primary trigonometric ratios (sine, cosine, and tangent) for angle $A$ in standard position. 2. **Recall definitions:** For an angle $A$ in standard position, the point on the terminal side of the angle is $(x,y)$ and the distance from the origin to this point is $r = \sqrt{x^2 + y^2}$. The primary trigonometric ratios are defined as: $$\sin A = \frac{y}{r}, \quad \cos A = \frac{x}{r}, \quad \tan A = \frac{y}{x}$$ 3. **Important rules:** - $r$ is always positive. - $\tan A$ is undefined if $x=0$. - The signs of $x$, $y$, and $r$ depend on the quadrant of angle $A$. 4. **Exact expressions:** - $\sin A = \frac{y}{\sqrt{x^2 + y^2}}$ - $\cos A = \frac{x}{\sqrt{x^2 + y^2}}$ - $\tan A = \frac{y}{x}$ These formulas give the exact trigonometric ratios for any angle $A$ in standard position based on the coordinates of the point on its terminal side.