Convert the given polar coordinates into rectangular coordinates. \( \left(2,270^{\circ}\right)=([?],[]) \)

To convert polar coordinates to rectangular coordinates, you can use the formulas \(x = r \cdot \cos(\theta)\) and \(y = r \cdot \sin(\theta)\). Here, \(r = 2\) and \(\theta = 270^{\circ}\). Calculating, we find: - \(x = 2 \cdot \cos(270^{\circ}) = 2 \cdot 0 = 0\) - \(y = 2 \cdot \sin(270^{\circ}) = 2 \cdot (-1) = -2\) Thus, the rectangular coordinates are \( (0, -2) \). Polar coordinates are beloved for their simplicity in representing points in a plane, especially in circular motion. The angle \(270^{\circ}\) points directly downwards along the negative y-axis, making it easy to identify that your rectangular coordinates will lie exactly at \(0\) on the x-axis and \(-2\) on the y-axis. For those enthusiasts who want to dive deeper, consider exploring the relationship between polar and rectangular coordinates in various applications. For instance, using polar coordinates simplifies problems in calculus like evaluating double integrals in circular regions, which can be quite a ride. Tackling these concepts enhances your understanding and helps prepare you for more advanced math adventures!