Convert to cartesian coordinates : (5,0), (5, pie)

To convert polar coordinates \((r, \theta)\) into Cartesian coordinates \((x, y)\), we use the formulas:

\[
x = r \cos(\theta)
\]
\[
y = r \sin(\theta)
\]

### 1. Converting \((5, 0)\)
- \(r = 5\)
- \(\theta = 0\)

Substituting in:
\[
x = 5 \cos(0) = 5 \cdot 1 = 5
\]
\[
y = 5 \sin(0) = 5 \cdot 0 = 0
\]

So, \((5, 0)\) in Cartesian coordinates is:
\[
(5, 0)
\]

### 2. Converting \((5, \pi)\)
- \(r = 5\)
- \(\theta = \pi\)

Substituting in:
\[
x = 5 \cos(\pi) = 5 \cdot (-1) = -5
\]
\[
y = 5 \sin(\pi) = 5 \cdot 0 = 0
\]

So, \((5, \pi)\) in Cartesian coordinates is:
\[
(-5, 0)
\]

### Final Answer:
- \((5, 0)\) in Cartesian coordinates is \((5, 0)\).
- \((5, \pi)\) in Cartesian coordinates is \((-5, 0)\).

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do polar coordinates relate to the Cartesian plane?
2. What if \(\theta\) is not a multiple of \(\pi\), how would the calculations differ?
3. Can the same Cartesian point have multiple polar coordinates?
4. What is the significance of \(r\) and \(\theta\) in polar coordinates?
5. How are negative \(r\) values interpreted in polar coordinates?

**Tip:** Remember that in polar coordinates, a positive \(r\) with an angle \(\theta + \pi\) points directly opposite to the angle \(\theta\).

Convert to Cartesian coordinates: (5,0), (5, pi)

Explore how to convert polar coordinates (5,0) and (5,π) to Cartesian coordinates. This problem demonstrates using x = r * cos(θ) and y = r * sin(θ) for precise conversions. Perfect for students in Grades 9-11 learning coordinate geometry.

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