1. **Problem Statement:** We want to find the equation of the line that connects the point on the circle given by coordinates $\left(20\sin(a), 20\cos(a)\right)$ and the fixed point $(-1,0)$.\n\n2. **Formula for the line equation:** The line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ can be written in point-slope form as:\n$$y - y_1 = m(x - x_1)$$\nwhere the slope $m$ is given by:\n$$m = \frac{y_2 - y_1}{x_2 - x_1}$$\n\n3. **Identify points:** Here, $(x_1, y_1) = (-1, 0)$ and $(x_2, y_2) = \left(20\sin(a), 20\cos(a)\right)$.\n\n4. **Calculate the slope:**\n$$m = \frac{20\cos(a) - 0}{20\sin(a) - (-1)} = \frac{20\cos(a)}{20\sin(a) + 1}$$\n\n5. **Write the line equation:** Using point $(-1,0)$, the line equation is:\n$$y - 0 = \frac{20\cos(a)}{20\sin(a) + 1}(x + 1)$$\nor simplified:\n$$y = \frac{20\cos(a)}{20\sin(a) + 1}(x + 1)$$\n\n6. **Interpretation:** This equation gives the line connecting the fixed point $(-1,0)$ to the rotating point on the circle parameterized by $a$. As $a$ changes, the point moves and the slope and line change accordingly.