1. **State the problem:** We need to find two angles in radians between $-2\pi$ and $2\pi$ whose terminal sides pass through the origin and a given point on the circle in the rectangular coordinate system. 2. **Recall the formula:** The angle $\theta$ in standard position that passes through a point $(x,y)$ on the unit circle satisfies: $$\theta = \arctan\left(\frac{y}{x}\right)$$ 3. **Important rules:** - The arctangent function returns values between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$. - To find the correct angle in all quadrants, use the signs of $x$ and $y$ or the $\text{atan2}(y,x)$ function. - Since the circle is periodic with period $2\pi$, angles differing by $2\pi$ represent the same terminal side. 4. **Find the first angle:** Calculate $\theta_1 = \arctan\left(\frac{y}{x}\right)$ or use $\theta_1 = \text{atan2}(y,x)$ to get the principal angle. 5. **Find the second angle:** The second angle with the same terminal side but within $-2\pi$ to $2\pi$ is: $$\theta_2 = \theta_1 \pm 2\pi$$ Choose the value that lies within the interval $[-2\pi, 2\pi]$ and is distinct from $\theta_1$. 6. **Summary:** The two angles are $\theta_1$ and $\theta_2 = \theta_1 \pm 2\pi$ within the given interval. This method uses the coordinates of the point on the circle to find the angles in radians whose terminal sides pass through that point.