Question

What are the rectangular coordinates of the point with polar coordinates (3, π/6)?

a) (3√3/2, 3/2)
b) (3/2, 3√3/2)
c) (3/2, √3/2)
d) (3√3/2, 3/2)

Answer 1

The rectangular coordinates of the point with polar coordinates (3, π/6) are (3√3/2, 3/2).

Step-by-step explanation:

The rectangular coordinates of a point with polar coordinates (3, π/6) can be found using the formulas:

x = r * cos(θ)

y = r * sin(θ)

Substituting the values r = 3 and θ = π/6 into the formulas, we get:

x = 3 * cos(π/6) = 3√3/2

y = 3 * sin(π/6) = 3/2

Therefore, the rectangular coordinates of the point are (3√3/2, 3/2), which corresponds to option a).