Plot the points with polar coordinates $\left(-5, \frac{2 \pi}{3}\right)$ and $\left(2,-\frac{11 \pi}{6}\right)$ using the pencil.
Solution
Step 1 ：Given two points with polar coordinates \((-5, \frac{2 \pi}{3})\) and \((2,-\frac{11 \pi}{6})\).
Step 2 ：The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
Step 3 ：The polar coordinates can be converted to Cartesian coordinates using the following formulas: \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\).
Step 4 ：Convert the given polar coordinates to Cartesian coordinates.
Step 5 ：For the first point \((-5, \frac{2 \pi}{3})\), the Cartesian coordinates are approximately \((2.5, -4.33)\).
Step 6 ：For the second point \((2,-\frac{11 \pi}{6})\), the Cartesian coordinates are approximately \((1.73, 1)\).
Step 7 ：\(\boxed{\text{Final Answer: The points with polar coordinates } (-5, \frac{2 \pi}{3}) \text{ and } (2,-\frac{11 \pi}{6}) \text{ are plotted on the Cartesian plane. The first point is located in the second quadrant with Cartesian coordinates approximately } (2.5, -4.33) \text{, and the second point is located in the first quadrant with Cartesian coordinates approximately } (1.73, 1).}\)
