Question

Given the point with Cartesian coordinates, (−7√3/2,7/2), find the polar coordinates of the point.

Select the correct answer below:


(7,4π/3)
(7,11π/6)
(3,4π/3)
(3,5π/6)
(3,11π/6)
(7,5π/6)

Answer 1

Answer: the last option is correct

Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:

r = √((-7√3/2)^2 + (7/2)^2)

θ = atan2(7/2, -7√3/2)

Simplifying the expressions:

r = √(147/4 + 49/4) = √(196/4) = √49 = 7

θ = atan2(7/2, -7√3/2)

Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:

θ ≈ 5π/6

So the correct answer is: (7, 5π/6), which is option (6).