Answer:
The rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3)
Explanation:
The given polar coordinates is (7, 2·π/3)
Where, the 7 represent the distance, r, from the point of reference and 2·π/3, the angle, θ, from the reference point.
Polar coordinates are represented in rectangular form by the equivalence transformation equation given as follows;
The x-coordinate = Radius, r × cos(θ), which gives
We note that 2·π/3 radians = 2 × 180/3 = 120°
x = 7 × cos(2·π/3) = 7 × cos(120°) = 7 × (-0.5) = -3.5
x = -3.5
The y-coordinate = Radius, r × sin(θ), which gives
x = 7 × sin(2·π/3) = 7 × sin(120°) = 7 × (√3)/2 = 3.5·√3
y = 3.5·√3
Therefore, the rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3).