Weston Reeves
09/19/2023 · Elementary School
The polar coordinates of a point are \( \left(9, \frac{\pi}{2}\right) \). Find the rectangular coordinates of this point.
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Step-by-step Solution
To convert polar coordinates \((r, \theta)\) to rectangular coordinates \((x, y)\), we use the following formulas:
\[
x = r \cos(\theta)
\]
\[
y = r \sin(\theta)
\]
Given the polar coordinates \((9, \frac{\pi}{2})\), we have:
- \(r = 9\)
- \(\theta = \frac{\pi}{2}\)
Now, we can calculate \(x\) and \(y\):
1. Calculate \(x\):
\[
x = 9 \cos\left(\frac{\pi}{2}\right)
\]
Since \(\cos\left(\frac{\pi}{2}\right) = 0\):
\[
x = 9 \cdot 0 = 0
\]
2. Calculate \(y\):
\[
y = 9 \sin\left(\frac{\pi}{2}\right)
\]
Since \(\sin\left(\frac{\pi}{2}\right) = 1\):
\[
y = 9 \cdot 1 = 9
\]
Thus, the rectangular coordinates of the point are:
\[
\boxed{(0, 9)}
\]
Quick Answer
The rectangular coordinates are (0, 9).
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