1. Problem: Given point $P(x,y)$, find exact values of $\sin \beta$ and $\cos \beta$ where $\beta$ is the angle formed by the line from origin to $P$ with the positive x-axis. 2. Formula: For any point $P(x,y)$, hypotenuse $r = \sqrt{x^2 + y^2}$. 3. Then, $\sin \beta = \frac{y}{r}$ and $\cos \beta = \frac{x}{r}$. 4. For $P(3,4)$: Calculate hypotenuse: $$r = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ Calculate sine: $$\sin \beta = \frac{4}{5}$$ Calculate cosine: $$\cos \beta = \frac{3}{5}$$ 5. Explanation: The hypotenuse is the distance from origin to point $P$. The sine is the ratio of the opposite side (y-coordinate) to hypotenuse, cosine is adjacent side (x-coordinate) to hypotenuse. Final answer: $$\sin \beta = \frac{4}{5}, \quad \cos \beta = \frac{3}{5}$$