Final answer:
The rectangular coordinates equivalent to the polar coordinates [3, π/3] are approximately (1.5, 2.598), calculated using the conversion formulas x = r ⋅ cos(θ) and y = r ⋅ sin(θ).
Step-by-step explanation:
To find the rectangular coordinates for a point given in polar coordinates [(3, π/3)], we use the conversion formulas:
- x = r ⋅ cos(θ)
- y = r ⋅ sin(θ)
For the given polar coordinates (3, π/3):
- x = 3 ⋅ cos(π/3) = 3⋅ (½) = 1.5
- y = 3 ⋅ sin(π/3) = 3⋅ (√3/2) ≈ 3⋅ 0.866 = 2.598
Thus, the rectangular coordinates equivalent to the polar coordinates [3, π/3] are approximately (1.5, 2.598).