Question

What is the Cartesian form of (3,−π/3)?

Answer 1

The Cartesian form of (3,−π/3) is (-3/2, -sqrt(3)/2).

Step-by-step explanation:

The Cartesian form of (3,−π/3) is (-3/2, -sqrt(3)/2).

In Cartesian coordinates, the x-coordinate represents the horizontal distance from the origin and the y-coordinate represents the vertical distance from the origin. In this case, the x-coordinate of (3,−π/3) is 3 and the y-coordinate is -sqrt(3)/2.

Therefore, the Cartesian form of (3,−π/3) is (-3/2, -sqrt(3)/2).

Answer 2

The Cartesian form of (3,−π/3) is (3/2, -3√3/2).

Step-by-step explanation:

The Cartesian form of (3, −π/3) can be found by converting the given polar coordinates to rectangular or Cartesian coordinates.

To convert from polar to Cartesian coordinates, we can use the formulas:

• x = r * cos(theta)
• y = r * sin(theta)

Using the values r = 3 and theta = -π/3, we can substitute them into the formulas to get:

• x = 3 * cos(-π/3) = 3 * (1/2) = 3/2
• y = 3 * sin(-π/3) = 3 * (-√3/2) = -3√3/2

Therefore, the Cartesian form of (3, −π/3) is (3/2, -3√3/2).