Problem

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 :\(\boxed{\text{Final Answer: The points with polar coordinates } (-5, \frac{2 \pi}{3}) \text{ and } (2,-\frac{11 \pi}{6}) \text{ are plotted on the Cartesian plane. The first point is located in the second quadrant with Cartesian coordinates approximately } (2.5, -4.33) \text{, and the second point is located in the first quadrant with Cartesian coordinates approximately } (1.73, 1).}\)

From Solvely APP
Source: https://solvelyapp.com/problems/7716/

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