To find the Cartesian coordinates $(x, y)$ from the polar coordinates $(r, \theta)$, we use the following conversion formulas:

$x = r \cdot \cos(\theta)$ $y = r \cdot \sin(\theta)$

Given the polar coordinates $(r, \theta) = \left(4, \frac{\pi}{2}\right)$:

1. For $x$: $x = 4 \cdot \cos\left(\frac{\pi}{2}\right) = 4 \cdot 0 = 0$

2. For $y$: $y = 4 \cdot \sin\left(\frac{\pi}{2}\right) = 4 \cdot 1 = 4$

So, the Cartesian coordinates are $(x, y) = (0, 4)$.

Would you like more details on the conversion or have any other questions?

Here are 5 related questions:

1. What are the Cartesian coordinates for polar coordinates $(5, \pi)$?
2. How do you convert Cartesian coordinates back to polar form?
3. What happens if the radius $r$ is negative in polar coordinates?
4. How does the angle $\theta$ affect the Cartesian coordinates when it is greater than $2\pi$?
5. Can polar coordinates be used in three-dimensional space?

Tip: When converting between polar and Cartesian coordinates, remember that the sine function affects the vertical direction (y-coordinate), while the cosine function affects the horizontal direction (x-coordinate).