https://file.aiquickdraw.com/mathbot/file/1732942227718k1vknhi8.jpg

To find the rectangular coordinates \((x, y)\) from the polar coordinates given, use the following formulas:

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

From the image:
- \( r = 2 \)
- \( \theta = \frac{5\pi}{6} \)

Now calculate:

1. **\(x\):**
\[
x = 2 \cos\left(\frac{5\pi}{6}\right)
\]
The cosine of \(\frac{5\pi}{6}\) is \(-\frac{\sqrt{3}}{2}\). So,
\[
x = 2 \times -\frac{\sqrt{3}}{2} = -\sqrt{3}.
\]

2. **\(y\):**
\[
y = 2 \sin\left(\frac{5\pi}{6}\right)
\]
The sine of \(\frac{5\pi}{6}\) is \(\frac{1}{2}\). So,
\[
y = 2 \times \frac{1}{2} = 1.
\]

Thus, the rectangular coordinates are:
\[
(x, y) = (-\sqrt{3}, 1).
\]

Would you like a detailed explanation or assistance with related concepts? 

Here are five related questions to explore:
1. How are polar and rectangular coordinates used in real-world applications?
2. Can polar coordinates be converted to rectangular coordinates if \(\theta\) is negative?
3. What are the reverse formulas to convert rectangular to polar coordinates?
4. How can you interpret angles like \(\frac{5\pi}{6}\) geometrically?
5. What are the key differences between polar and rectangular coordinate systems?

**Tip:** Always

A point is graphed in polar form. Find its rectangular coordinates.

Learn how to convert the polar coordinates (2, 5π/6) to rectangular coordinates using trigonometric functions. Detailed step-by-step solution provided, covering the concepts of sine and cosine. Ideal for high school math students.

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