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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).

Find the Cartesian coordinates of the point whose polar coordinates are: (r, θ) = (4, π/2).

Learn how to convert the polar coordinates (4, π/2) into Cartesian coordinates using trigonometric formulas. The solution explains the steps clearly, including the calculation of x and y using sine and cosine functions.

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