In the polar coordinate system, what is the name for a set of coordinates such as the one indicated with $c$ (for example, $(r,\theta )$)?

• A. Rectangular coordinates
• B. Parametric coordinates
• C. Polar coordinates
• D. Cartesian coordinates

Answer: (C)

Verified step by step guidance

1. Understand that the problem is asking for the name of a coordinate system represented by pairs like \((r, \theta)\), where \(r\) is the distance from the origin and \(\theta\) is the angle measured from the positive x-axis.
2. Recall that in the rectangular or Cartesian coordinate system, points are represented as \((x, y)\), which are distances along perpendicular axes.
3. Recognize that parametric coordinates refer to expressing coordinates as functions of a parameter, not a coordinate system itself.
4. Identify that the coordinate pair \((r, \theta)\) corresponds to the Polar coordinate system, where \(r\) is the radius (distance from origin) and \(\theta\) is the angle.
5. Conclude that the set of coordinates like \((r, \theta)\) is called Polar coordinates.