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.