Question

Convert the polar coordinate (2, (5π)/6) to rectangular coordinates.

a) (1, √3)
b) (√3, 1)
c) (-√3, -1)
d) (-1, -√3)

Answer 1

To convert polar coordinates to rectangular coordinates, use the formulas for x and y. Plug in the given values to find the rectangular coordinates.

Step-by-step explanation:

To convert polar coordinates to rectangular coordinates, we can use the formulas:

x = r * cos(theta)
y = r * sin(theta)

Given the polar coordinate (2, (5π)/6), we can substitute the values into the formulas to find the rectangular coordinates:

x = 2 * cos((5π)/6) = 2 * (-√3/2) = -√3
y = 2 * sin((5π)/6) = 2 * (1/2) = 1

Therefore, the rectangular coordinates are (-√3, 1). Option c) is the correct choice.