Bowen Greene
03/03/2023 · Middle School
The rectangular coordinates of a point are \( (-16,0) \). Find the polar coordinates.
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Tutor-Verified Answer
Step-by-step Solution
To convert the rectangular coordinates \((-16, 0)\) to polar coordinates \((r, \theta)\), we use the following formulas:
1. The radius \(r\) is given by:
\[
r = \sqrt{x^2 + y^2}
\]
where \(x = -16\) and \(y = 0\).
Substituting the values:
\[
r = \sqrt{(-16)^2 + 0^2} = \sqrt{256} = 16
\]
2. The angle \(\theta\) is calculated using:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Since \(y = 0\) and \(x = -16\), we have:
\[
\theta = \tan^{-1}\left(\frac{0}{-16}\right)
\]
The tangent of \(0\) is \(0\), and since the point is located on the negative x-axis, the angle \(\theta\) is:
\[
\theta = \pi \text{ (or } 180^\circ\text{)}
\]
Thus, the polar coordinates of the point \((-16, 0)\) are:
\[
\boxed{(16, \pi)}
\]
Quick Answer
The polar coordinates of the point \((-16, 0)\) are \((16, \pi)\).
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