Question

Convert the polar coordinates (5, 3π/2) to rectangular coordinates.

Answer 1

To convert the polar coordinates (5, 3π/2) to rectangular coordinates, apply the formulas x = r×cos(θ) and y = r×sin(θ) to obtain the rectangular coordinates (0, -5).

Step-by-step explanation:

The student has asked to convert the polar coordinates (5, 3π/2) to rectangular coordinates. To convert polar coordinates to rectangular coordinates, you use the formulas x = r×cos(θ) and y = r×sin(θ), where 'r' is the radius (distance from the origin), and 'θ' is the angle in radians measured from the positive x-axis.

In this case:

• r = 5
• θ = 3π/2 radians

Applying the formulas:

• x = 5×cos(3π/2) = 5×0 = 0
• y = 5×sin(3π/2) = 5×-1 = -5

Therefore, the rectangular coordinates are (0, -5).