3π/4 (-√2/2, √2/2)
The rectangular coordinates of the point (3π/4, (-√2/2, √2/2)) are (- (3√2π/8), (3√2π/8)).
The given point in polar coordinates is (3π/4, (-√2/2, √2/2)). To convert polar coordinates to rectangular coordinates, we can use the following relationships:
x = r cosθ
y = r sinθ
where r is the radius and θ is the angle of the point.
In this case, we have:
r = 3π/4
θ = 3π/4
x = r cosθ = (3π/4) cos(3π/4) = -(3π/4)(√2/2) = – (3√2π/8)
y = r sinθ = (3π/4) sin(3π/4) = (3π/4)(√2/2) = (3√2π/8)
Therefore, the rectangular coordinates of the point (3π/4, (-√2/2, √2/2)) are (- (3√2π/8), (3√2π/8)).
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