To convert polar coordinates to rectangular coordinates, we can use the formulas:
- x = r × cos(θ)
- y = r × sin(θ)
Here, r is the distance from the origin, and θ is the angle in radians.
Given the polar coordinates (3, 3π/2):
- r = 3
- θ = 3π/2
Now, we can plug in the values into the formulas:
Calculating x:
- x = 3 × cos(3π/2)
- Since cos(3π/2) = 0, we find that:
- x = 3 × 0 = 0
Calculating y:
- y = 3 × sin(3π/2)
- Since sin(3π/2) = -1, we find that:
- y = 3 × -1 = -3
Thus, the rectangular coordinates corresponding to the polar coordinates (3, 3π/2) are:
- (x, y) = (0, -3)
In conclusion, the conversion of the polar coordinates (3, 3π/2) results in the rectangular coordinates (0, -3).