Question

Plot the point given in polar coordinates and find the corresponding rectangular coordinates for the point. $$ (4,3 \pi / 6) $$

Short answer

The rectangular coordinates for the polar coordinates (4,3π/6) are (\(2\sqrt{3}\), 2).

Step-by-step solution

Understand the given polar coordinates

The polar coordinates given are (4,3π/6), where 4 is the distance from the origin (r) and 3π/6 is the angle from the positive x-axis (θ).

Convert polar coordinates to rectangular coordinates

Use the formulae x = r cos(θ) and y = r sin(θ). Here, x = 4 cos(3π/6) and y = 4 sin(3π/6). So, the rectangular coordinates are (\(2\sqrt{3}\), 2).

Plot the point on the Cartesian coordinate system

Draw two axes, the horizontal one being the x-axis and the vertical one the y-axis. Go right from the origin \(2\sqrt{3}\) units along x-axis and up 2 units along the y-axis and place a dot. The plotted dot represents the point with rectangular coordinates (\(2\sqrt{3}\), 2).