Convert the point to rectangular coordinates.
$(4,\(\frac{\pi}{6}\))$

• A. $(2\(\sqrt{3}\),2)$
• B. $(4\(\sqrt{3}\),4)$
• C. $(2,2\(\sqrt{3}\))$
• D. $(2,\(\sqrt{3}\))$

Answer: (A)

Verified step by step guidance

1. Understand that the given point (4, \(\frac{\pi}{6}\)) is in polar coordinates, where 4 is the radius (r) and \(\frac{\pi}{6}\) is the angle (θ) in radians.
2. Recall the formulas to convert polar coordinates to rectangular coordinates: x = r \(\cos\)(θ) and y = r \(\sin\)(θ).
3. Substitute the values into the formulas: x = 4 \(\cos\)(\(\frac{\pi}{6}\)) and y = 4 \(\sin\)(\(\frac{\pi}{6}\)).
4. Calculate \(\cos\)(\(\frac{\pi}{6}\)) and \(\sin\)(\(\frac{\pi}{6}\)). These are standard trigonometric values: \(\cos\)(\(\frac{\pi}{6}\)) = \(\frac{\sqrt{3}\)}{2} and \(\sin\)(\(\frac{\pi}{6}\)) = \(\frac{1}{2}\).
5. Multiply the radius by the trigonometric values: x = 4 \(\times\) \(\frac{\sqrt{3}\)}{2} and y = 4 \(\times\) \(\frac{1}{2}\). Simplify these expressions to find the rectangular coordinates.