Question

Convert the polar coordinate $(7, 11 \pi/6)$ to Cartesian coordinates.

A) $(7\sqrt{3}/2, -7/2)$
B) $(7\sqrt{3}/2, 7/2)$
C) $(-7\sqrt{3}/2, -7/2)$
D) $(-7\sqrt{3}/2, 7/2)$

Answer 1

To convert the polar coordinates (7, 11\(\pi\)/6) to Cartesian coordinates, one calculates the x and y components using trigonometric functions to get the Cartesian coordinates (7\(\sqrt{3}\)/2, -7/2), which matches option A.

Step-by-step explanation:

The conversion of polar coordinates (7, 11\(\pi\)/6) to Cartesian coordinates involves the use of the formulas x = r\(\cos\)(\(\theta\)) and y = r\(\sin\)(\(\theta\)), where r is the radius and \(\theta\) is the angle in radians.

• First, calculate the x-coordinate:
• x = 7\(\cos\)(11\(\pi\)/6) = 7\(\cos\)(330\(^\circ\)) = 7\(\sqrt{3}\)/2
• Next, calculate the y-coordinate:
• y = 7\(\sin\)(11\(\pi\)/6) = 7\(\sin\)(330\(^\circ\)) = -7/2

The Cartesian coordinates are (7\(\sqrt{3}\)/2, -7/2), which corresponds to option A.